Computer won't turn on

I turned off my computer so I could vacuum yesterday (turning the vacuum cleaner even manages to dim the lights), but when I finished and went to turn it back on, I couldn't.

No lights, no fans, not a single sound. (Yes I made sure the little flip on the back of the PSU was on and that the power strip was working).

I swapped the PSU with the one from the family computer, and... still no go. Am I right in assuming that the problem does not lie with the PSU then? How do I check to see if it's another issue, like the motherboard/CPU? I've read that sometimes the power on button craps out, but I have no idea how to check that.

This is like the second time this year my computer's had a major crap out, so annoying.

Any help or suggestions you guys can give me would be great.

Here are some of my crappy computer specs, if they are helpful:

P4 2.4GHz
512MB RAM
450w PSU
ATI Radeon 9200 SE
I put the computer together about 2.5 years ago, so it's not a pre-assembled one.

Also a random tidbit of info:

Starting from maybe half a year ago, if I was playing Ragnarok Online or Albatross18 or something, the screen would start getting staticy, I'd hear the whir of a fan going crazy and then it would power down. This happens without fail unless I remove the side case and direct a large fan (like a desk fan) straight into the case. I thought it was the graphics card that was screwing up, but it's flawless every other time. Plus it doesn't have a fan on it to start with, so... Is that indicative of the CPU overheating or something? Might that have something to do with my current problem?

Sorry for the tl;dr. Thanks!

Jam it back in, in the dark.