Wow  , so I finally able to get my Electrum updated, which was a whole thing (long story). After that I was able to follow the steps above to create a transaction and push it to Eligius. I didn't think it worked because it took about 12 hours, but finally the transactions went through. Thanks for the guidance everyone!

Do you know how to do that by any chance? In searching for help, I'm not really finding any info on how to actually use Electrum console commands, and whatever info I have found is way above my pay grade, so to speak.

Yes, I checked 5 block explorers, and the transactions do still appear on Blockchain.info, Insight, TradeBlock and Blocktrail, but they don't exist on Blockr.io. On Blockr.io I get "this transaction is unknown." So what does that indicate? I tried switching servers anyway, but it did nothing.

How would I go about that? Trying some Googling now, but this may be over my head.

Also, the receiving wallet isn't showing these pending transactions anymore. They disappeared from the transaction history there, but they're still stuck on pending in the sending wallet. What does that mean?

Is it at all possible to do a child pays for parent type thing from the sending wallet of a pending transaction, or can it only be done from the recipient?

Thanks. I think I understand a little more what I'm supposed to do. The issue I'm facing at the moment is related to the particular client I'm using, I think. In the Electrum client that I'm sending from, I see the option in the preferences to "Check transaction before broadcasting," so I know what I'm looking for, but I don't see that option in the version of Electrum that's on the receiving end of the pending transactions. The original transactions were from a wallet on one computer to a wallet on another, and the second computer is using the Linux Electrum client, which apparently doesn't have this option? Hopefully that makes sense. Long story short, I don't see any option for signing or checking transactions or exporting them. All it appears I'm able to do, as far as I can tell, is send a transaction directly using the "send" button.

Thanks for the reply. I kinda get the idea, but I'm hoping for instruction that takes no knowledge for granted. In other words, explain like I'm 5. Some things are unclear to me, like when you say "Step 3: Create a transaction that spends the unconfirmed transaction to another Bitcoin address.", I assume you mean from sending from the receiving end of the original pending transaction, right? Can this be an address from the same wallet (for the receiving wallet in Electrum, I have 5 different receiving addresses, but I think they're all the same wallet?), or does it have to be the exact address the pending transaction was sent to? Furthermore, in step four, how do you sign the transaction and send it through Eligius? In Electrum, it only allows me to simply send to another wallet address, but I don't see any options to do anything more specific than that. I couldn't find an answer through Google. Or do I have to use something other than Electrum?

So I have multiple pending transactions in Electrum that have been sitting with zero confirmations for four days now. I've had other transactions go through since then, but on these I apparently didn't use enough of a transaction fee. On another site, someone suggested I try "child pays for parent" and pointed me to https://bitcointalk.org/index.php?topic=729535.msg8251404#msg8251404. Now, I'm a total newbie, just started with bitcoin like a week ago. I sorta understand the concept being described in that post, but I'm not sure I follow the process. It's just vague enough to be confusing to someone who doesn't know what they're doing. For example, right away in step 1, it refers to a different transaction than the one the OP of that thread originally asked about. What's the connection there, and why does it come into play later as well in step 3 where there are now three transactions involved? And in step 2, do I have to send it back to the original sending address, or literally just any other address?

The person referring me here didn't know enough to help me further, so I thought I'd come to the source. Basically, it would be amazing if someone could give me an idiot proof blow-by-blow of the process. Maybe I could follow it better using using one of my pending transactions as an example, like this one: https://blockchain.info/tx/d98144e300e6a119ed54a47df73c3ead075d00f1fb2417f952c4dcd4ad6752fe