BEst thing to do is turn it off, disconnect the PS, ground yourself, and start unseating and reseating all of the removables. HDD cables, Ram ships, PCI cards, large IDE cables connected to mobo, you name it. Blowing it out sounds like a great idea. You may want to consider adding a fan or two. If none of those work, check to see if there is a BIOS update, or some other 'critical' update at HP's site. It sounds to me like it is either overheating, or you mobo maybe bad. I saw very similar behavior in a Dell laptop that had a bad mobo. But also seen it while running hot temps, after replacing RAM, or trying to get a failed hdd to fly.
Mr. Godwin, if you ever plan on upgrading your PC it is wise to get the biggest, beefiest PS you can afford. The Antec's are decent. I went low and got a Thermaltake 430w when I bought my parts about 4 years ago now. Today I would try to get a 500w, just to be safe.