Over a year ago I noticed problems with an aging computer. I'd been having trouble with high heat for a long time. I most noticed it when playing MTW2 in custom battles. It shut off and I couldn't get it to come back on.
Opening it up, the thermal paste had separated from the heat sink. As such the graphics driver board was getting entirely too hot and one of the many safeties on temperature had caused the kickout. After a good cleaning, I purchased an inexpensive thermal paste, probably a better one than the original with silver in it (heat conducting but not electrically conducting). After I did this, I no longer had any issues with it. It actually is running better than it was originally even in intense battles with no lag.
It's possible that one of those safeties is keeping your computer from booting.
Here's a step by step guide on checking/replacing it.
http://www.instructables.com/id/How-...rmal-Paste-on/
At a certain point, you might need a computer tech, but I can tell you honestly that some will just try swapping out boards to isolate the issue and that can get expensive.
Have you tried an outlet that is entirely seperate from the standard one? I had a very strange breaker issue where low power was coming through a breaker once and causing undervoltage to the device. That took forever simply because I didn't try going to another room outlet for troubleshooting. I scratched my head for the longest time over that one.