We have a desktop HP (coming up on 3 years old). It had been off for a few weeks. Today when we attempted to boot it, it started... gets as far as allowing a login sometimes, others it does not... then it acts as if it powers down... video feed to monitor goes off, power to USB speakers stops and the keyboard locks (no lights work, no beeps on holding ESC). Nothing works, including pressing and holding the power button to do an actual power off. You physically have to unplug the base to get it to shut off. And even then, the power light stays on for 5-10 seconds after unplugging before it finally goes out. This happens in ALL modes... Safe, safe with networking... all of them.
Personally, I am thinking it may be a power supply problem... But wanted a second opinion.