Think I had a virus or trojan

Chryslerfat: To me this definitely sounds like a hardware problem, either power supply or motherboard. You don't have an ASUS motherboard, as a previous post suggested a bios issue. When I did PC work on the side, I had a client's computer (small form factor HP desktop, no less), where I narrowed the issue to one of those two (can't remember the symptoms). Because HP uses proprietary hardware, either of the parts was hideously expensive. As the PC was a few years old, I recommended replacing the unit with new.
Since your computer DOES power up eventually, I'm almost 100% certain you are looking at a bad power supply. But again, an HP unit might cost $100 or more. Not worth it for a 5 year old PC, in my opinion. My suggestion? Leave the machine running all the time. I think the hot and cold cycling of the capacitors inside the PS is the issue. Let them stay hot, and you might go on for a good long time this way. As always, back up important files regularly.