Well, I called the Geek Squad. After talking with them and hearing "wow, that IS weird" several times, and after hearing that it's $199 just for them to come out and diagnose the problem (solving it would add quite a bit to the bill), we decided to make a quality of life call on the computer. It's hard to put our beloved electronics down, but eventually we have to make that choice.
Given that this is not the first PC I've had that has waited just months after the warranty expired to fizzle, I am converting to (gasp) a Mac. E has been trying to get me to convert to Apple since we met. It wasn't his overwhelming logic that decided me, it was fail after fail of my PCs. Apple was running a special, so it wont impact our overall budget too much, and we'll have fewer cords to worry about Loki chewing on. Plus, I will still have the programs I like and need to use (word and excel).