Maximum PC

I have a PC that I built myself about 3 years ago. A few days ago it wouldn't power on. It actually just barely starts to power on... I can see a fan start to spin up. Then after a second or two, the fan starts slowing down and stops. So clearly it's getting some power.

I've ordered a power supply replacement so I should soon know if that's the problem, but my understanding was that before a power supply failed, you usually see lockups and shutdowns, and that hadn't been my experience. I sometimes had trouble booting but once it booted, it would run fine for hours.

Any ideas (other than replacing the power supply)?

thanks - Dave