Can I get a copy of a "for test" electrum.dat (wallet) file from version 0.30? (or share a download link for everyone)
Because I'd like to play with it using various tools, also to be able to test some options for OP.

Also, have you found an option to export the private keys in Electrum version 0.3?

That's certainly normal (since it's IanColeman's compression tool, it must be P2PKH).
Although both correspond to the same Private Key, Bitcoins aren't stored using the private key but through a "locking script" which is represented to you by an address.
So simply by knowing that the compressed and uncompressed addresses are different than each other explains why each has different balances because the bitcoins are locked using different scripts.

The HASH160 which is part of the locking script is derived from the public key.
Compressed and uncompressed public keys are different from each other (as you can seed in the tool) so both wont produce the same HASH160 result,
thus, different locking scripts for the compressed and uncompressed.

If that's the case, then the error must be a mistook character (eg.: letter case).
There's no way Bitcoin Core will return with that error if the WIF private key is correct.

It's quite easy to check for the wrong character since the WIF private key should only have BASE58 characters which shouldn't contain any I, l (lowercase L), O (uppercase o) or 0 (zero).
See if it has any of those characters and replace them with the similar character from the list below.
It should only have: https://en.bitcoin.it/wiki/Base58Check_encoding#Base58_symbol_chart (strictly case sensitive)

You can use Electrum as an interface for Ledger, just follow their guide to create an Electrum wallet using your Ledger.
support.ledger.com/hc/en-us/articles/115005161925-Set-up-and-use-Electrum?docs=true

Then use sweep (Wallet->Private keys->Sweep) to send all of the private key(s) available balance to your Ledger.

Yes but not directly using the paper backup,
you can restore the backup, export the private key(s) from Armory and import it to another client.

HCP has a post with steps about exporing keys from Armory: https://bitcointalk.org/index.php?topic=4746784.msg43255691#msg43255691
Note: Armory doesn't have to be online or synced to export the private keys.

Then in the other client, find an option to import or sweep your private keys.

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But if the restored wallet is empty in Armory, there's a great chance that the exported private keys are holding no coins either.

This is concerning since the error indicates that there's an issue with the provided private key.
My suggestion below will only work if your private keys is valid.

You can set-up a cold-storage Electrum to fulfill that, create an imported Electrum in your Cold-storage PC and create a watch-only imported Electrum to the online PC.

Here are the simple steps:

• Download Electrum from electrum.org | I also recommend you to verify its signature: how-to-verify-your-electrum-download
• Install Electrum on both PC.
• In the offline PC, create a wallet using the option in the installation wizard: "Import Bitcoin addresses or private keys"
• Type the private key in the box, click next and finish the set-up, that should create an [imported] wallet.
• In the online PC, select the same options but paste the address instead. It will create an [imported - watching only] wallet.
• Wait for the balance to show in the online PC, then create a transaction that sends the funds to your hardware wallet, an advanced preview will display after clicking 'pay->send'.
• In the advanced transaction preview, click "Export", then "Export to file", a (.psbt) file will be created to the selected directory, transfer it to your offline PC.
• Back to the offline PC, load the transaction file using Electrum's menu "Tools->Load transaction->From file", the advanced transaction preview will show.
• Click "Sign" and then use the same export options to export the signed transaction, transfer the signed raw transaction (.txn) to the online PC.
• Back to the offline PC, use the same load transaction options to load it and in the advanced preview, [review everything especially the output address(es) and fee] click "broadcast" to finally send the transaction to the network.

You can't use that option anyway since Windows Bitcoin Core wont be able to serve the pruned blocks to the Bitcoin Core on your Mac.

The script type isn't important when recovering funds in Bitcoin core because it can look for all types when scanning for balance.
So if you've successfully imported the private key, it should be able to restore the previous balance once Bitcoin Core finished the rescan.

You shouldn't include the <> in "<my private key>";
but if you typed it correctly, then you've included invalid characters to your private key. It should start with K or L consisting of 52 characters.
example command:

Question: is your Bitcoin Core fully synced to the network after the reinstall? Have you disabled "prune" settings?

Unfortunately yes, aside from the file's timestamp itself, the only indication of a possible date is the block height in the dump file (dumpwallet) when it's last used
and since you've loaded it in 2017, it will show you a block height of 2017.

But since it's created on 2011~2013, one loose indicator that it's that old is if the wallet isn't "HD" (has a slash at the HD logo at the lower-right hand side of Bitcoin Core UI)
It will stay that way unless the wallet has been upgraded into HD by setting an 'HD Seed' through sethdseed command.
In comparison, wallets created by 2017 Bitcoin Core versions are HD.

Does the 30-character "password" looks similar to a "mini private key" as described in this topic:
[overview] Recover Bitcoin from any old storage format ?

If so, try to import it to Electrum (electrum.org) and see if it will restore the address listed in your paper.
[Take your time to verify Electrum's signature before using it for extra security | Select the option "Import bitcoin addresses or private keys" when creating a wallet]

Regardless of the date: if it's from versions lower than v0.31, then your seed phrase can't be used to recover the wallet to the later versions.

These are the "release notes" that came with Electrum v0.32 and some later versions:

TL;DR: It indicates that there were two updates that made the very old electrum wallets unrecoverable with the later versions,
seed should still work but it will generate a different set of keys hence will recover a 0 balance wallet.

Your option is to install v0.30 below, restore your seed phrase, then dump the private keys from the wallet file.
IDK if there are wallet tools that support it though, perhaps some old timer has some info.

This is just for the mentioned features;
but if you wish to get rid of the error, just install ecdsa package through pip: pypi.org/project/ecdsa

That indicates that the wallet.dat may be corrupted, also Bitcoin Core throws a similar error so that should confirm it.

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I think you need to start your own thread in Bitcoin Technical Support board for corrupted wallet.dat recovery options.
Link to the board: http://bitcointalk.org/index.php?board=4.0

I'm sorry but you're in the wrong board to ask online wallet-related questions.

You can go to web wallets board, then create a new thread (click "new topic" at the right),
link to the Web-wallets: https://bitcointalk.org/index.php?board=222.0

In that case, do not use --datadir and put ".\" before "wallet.dat";
that will tell pywallet to look for the wallet.dat file in the working directory:

The config file should be in the default data directory which is the former.
The latter is the installation directory which wont be used as the datadir by Bitcoin Core, unless told to do so.

The line "datadir" in the config should tell Bitcoin Core to create the files into that folder so there may be something that's causing it to use "E:\" instead of "E:\Bitcoin".
It can be overridden by the -datadir start parameter so check if you're still using an old shortcut.

Or the config file may actually be "bitcoin.conf.txt" which is caused by Windows explorer not showing the extension (enabling "File name extensions" will do the trick).
In which case, it will use what's set in the GUI.

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You can also try to use the old directory if you don't want to restart from scratch,
rename it into the folder name that you want and put the path into the datadir= line in the config file.

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Do not forget to close Bitcoin Core to apply the new config.

That was odd, because AFAIK there's no official Windows binary of Electrum in 2011.
Have you somehow used BTCurious' non-official Windows binaries? (/index.php?topic=50936.msg641963#msg641963)

Anyways, there's no way to get into your wallet without those since Electrum isn't kind of a custodial service where your "account" is hosted in a server.
And even if you get the seed phrase, it will still be troublesome to recover the wallet since it suffers to a derivation bug and will generate different keys when restored to the latest version.

You can check if you have more than one wallet in Electrum in the menu: "File->Open" or "File->Recently open".
Sometimes, newbies tend to use another wallet for their "missing transactions".

If you only have one wallet, then it's most likely a clipboard-hijacking malware/virus that changes the address that you've copied or you installed a fake version of Electrum.
(see the other replies to check if you are infected with the malware | verify your downloaded Electrum to see if it's legit)
But neither of those can recover your lost bitcoins, that's to know the culprit.

Are the addresses' script type in the website the same as Electrum's?
In simple words, do the addresses start with 1, 3 or bc1 in both Electrum and website?

Because some merchant API can generate different script type if loaded with an "xpub" from electrum's legacy wallet.

It will be grayed-out in that 'Open Wallet' list if it's loaded
and the wallet should be selectable in the "Wallet:" drop-down menu at the right-hand side of Bitcoin Core:

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If the PM is about sending the wallet.dat, please don't send it to anyone including me.

Problem is, OP didn't followed anything based from his last reply (which I replied to).
My reply has different goal, it is to cross-check the actual address that he typed in localbitcoins with his Electrum's receiving address.
Plus (in my reply's case) why would you have to go to a blockexplorer if you can already see the transaction's output in the app/website itself?