This morning, Skype still couldn't send any of the messages stuck in its queue. However, I was able to send some messages to people I haven't messaged in a while (at least, it didn't start showing that the messages were pending, so I assume they went through. Got no responses yet), so it may just be an issue with the Echo service and one or two people I had active conversations with when the problem started. This would be an issue, since the reason I had active conversations with them was that I have business with them in the near future that needs to be conducted via Skype. Fortunately, calls to the Echo service still work, so in the worst case, I can probably just call them and let them know what's going on. Meanwhile, it's not a problem with the local Skype install or the network, so I may try removing them from my list and re-adding them. I just worry because that takes place via the same interface as messaging, so if it still doesn't work, I may lose the ability to call them completely. Hopefully, it's just something to do with the local storage of how to communicate with them that's corrupted, and removing that would fix the problem. I'll have to try it with the Echo service first, if that can even be removed.
I hate technology sometimes. At least I finally got back to God of War 3 last night, and while I didn't make much progress, I'm at the part of the game where any progress is a huge leap forward.