There is indeed a simple explanation.
Let me try to explain in as simple terms as possible (without going in a lot of technical details).
First of all there are two separate "files" on a bitcoin system: you've got the block-chain and you have a wallet.
The "block-chain" records all transactions of everybody and it is updated every time your bitcoin client receives a new block.
The "wallet" is your personal file and contains two important things: the private keys of all your bitcoin addresses (so you can prove to the network you "own" that bitcoin address and nobody else should be able to do transaction on your behalf) and a list of transactions related to those bitcoin addresses.
Your "wallet" file is checked each time a new block arrives: if the new block contains transactions to any of your bitcoin addresses, those transactions get "copied" to your wallet. This is to prevent that each time you want to use one of your bitcoin addresses, the whole block-chain must be scanned to get your balance.
Now, the "normal way of using bitcoin":
1. You generate an address (it gets inserted in your wallet)
2. You sent or receive some coins to that address
3. As soon as those transactions are received by your client, you'll see the balance change (with 0 confirmations)
4. As new blocks arrive, you get more and more confirmations.
You don't have to be on-line during phase 2, because when you get your client on-line again, it'll continue downloading the block-chain/transactions where it last left, and "nothing will get lost".
Now in your case, you don't follow these scheme at all: on that "different computer" you have a client running that doesn't know (yet) your new address, so in phase 3 when the client receives those transactions/blocks, it just records them in the block-chain and doesn't update any wallet (not the current wallet as it doesn't contain your bitcoin address, nor your wallet on the pen drive). Then you copy your "secure" wallet to that client. Nothing will happen, as the block-chain end is already way passed the block that contains the transactions of your "secure" bitcoin address.
In fact, now the optimization of not scanning the entire block-chain each time you want to see the balance of your bitcoin addresses, is playing against you.
But don't despair, a few versions ago, a new command was introduced just for this case: the "-rescan" option when you start your bitcoin client. It will rescan the whole block-chain (and it will now find the "lost" transactions of your "secure" wallet)
Hey guys, thanks a lot for the quick response. Is that something I should type somewhere?? Sorry for the non-existent tech skills (Treat me as I'm 2)
(I will look into moving to linux Kimasa, thanks for the heads up)
If you don't know how to open a command prompt in Windows 7, you can use the following to get the rescan option to work:
Go into the start menu and find the Bitcoin program (Start -> All Programs -> Bitcoin -> Bitcoin).
Instead of clicking it normally, use the right mouse button and from the pop-up menu, select "Properties".
You should see in "Target" something like "C:\Program Files\Bitcoin\Bitcoin.exe". Inside the quotes, add the ' -rescan' text (without the single quotes, and pay attention to the space, so that it reads at the end: bitcoin.exe -rescan"
If that works fine, remove the " -rescan" again, otherwise each time you'll start bitcoin, it'll do a rescan.
Hope this helps.