Having a strange problem with my Compaq Presario/AMD Athlon (1.5 yrs old). As long as it's running, everything is fine. But, if you shut it off, for any reason, and pull power, even for an instant, it won't restart.
Looking at the power supply on the back, I noticed that the power led (on the power supply) was blinking intermittently. So, I plugged in a spare (working) supply, to no avail. But, I put AC back to the old (still installed) supply, and the light came on.
Through trial and error, I learned that, when the motherboard power connector is plugged in, the computer simply won't start (no lights, no noise, NOTHING) and the power supply led blinks. But, unplug that, and the light is on.
Just to see I tried plugging in the motherboard cable with the AC connected. Okay, not the brightest thing to do, but I wanted to see, and sure enough, as soon as you plug in the connector from the motherboard to the power supply, the light goes to blinking. Note that it's not like an "error code blink", just an intermittent flash of varying intensity.
If you plug and unplug the AC cord a few times (tried 2 ac cords to eliminate that problem) the light will finally stay on, and the computer will work fine, until the next power flash.
I figure I can either puzzle this out, or just go buy a battery backup:-)