Hi guys,
Sorry to abandon you. I do appreciate all the input. I finally found some time 2 weekends ago to go in and clean out everything, dust, and have a general look around. My motherboard appears to be normal to my untrained eye. I don't notice any bulging or leaking capacitors. I unscrewed the power supply from it's place on the tower, and make sure that that was cleaned out too (the fan is on the bottom, so it's hard to get at). I did notice that my heatsink was pretty dirty, so in messing with cleaning that, I broke one plastic (ugh, why plastic?) holding pin. And another one was already broken on the same side.
When I fired my computer back up after cleaning, it's having problems. It runs anywhere from zero to 10 minutes and just shuts off (zero meaning it wont fully boot). I'm guessing that this is because my heatsink isn't sitting flush so it's probably not working properly, and the system is shutting down to prevent processor damage. Interestingly, the longest run times have been when the tower was laying on its side, with gravity probably helping the heat sink connection. I have a new heatsink coming and it should be here next week. If that doesn't work, I'm thinking that the power supply could have a short in it (I was flexing the cords some), so I might as well replace that. And if that doesn't work, it's got to be the motherboard, right?
Crap! I went from thinking about upgrades to just wanting the thing to keep working in the span of 2-3 weeks. It'll be another week before I can get the new heatsink on, so I guess I won't know much right away, but I didn't want this to get buried too much.