Computer will not power up

For the front panel power button to cause this type of behavior, it would need to short out.

Pull the power switch leads from the motherboard.
Leave them off for several seconds.
Then push them on and remove them.

If the system powers up, the power switch is bad.

If the system does not power up, try the same again, except use a jumper lead.

Next, remove ALL plug-in cards except your video card, and see if the system powers up.

If it still does not power up, the culprit is one of 3 items:

Power supply,
Motherboard,
CPU

Since the power supply is the least expensive and easiest to swap, try that first.

If it is not the power supply, you need to decide how much time and effort you wish to put into this.
Also, IF the motherboard itself failed, it could destroy every CPU you plug into it.

Find the least expensive used known good CPU that will work with your motherboard.

If that fixes things, you need a new CPU.
If not, the motherboard is the next suspect.

Chas

To add to Chas's comments I would first be considering the PS as a first option but from my reading of your original post I took it that you are leaving this on 24/7 is that correct?

If that is what you have been doing the most likely culprit is that there is an overheat problem occurring as you didn't mention what type of M'Board CPU you are using did you apply any Heat transfer Paste between the Heat sink & CPU? Did you need to? Are you sure that the Heat Sink is making a good contact with the CPU I've seen several on the older Socket 370 or Socket A where the Hat sink has been put on the wrong way and only been making partial contact with the CPU as the other side of the socket is holding it off the CPU if that is the case you've most likely fried the CPU as it was never allowed to be cooled properly.

Instead of turning off the ATX Power switch pull the cord and leave it disconnected for several minutes and see if that makes any difference when you plug it back in it's possible that you are toward the end of the mains in your area and that some heavy ripples are coming over the mains and causing the system to hang or in this case shut down with a scrambled CPU.

I had a problem like that at one company who where very close to a newspaper and overtime that they started their printing presses their server would fall over it also set off the Burglar Alarms as well but that wasn't my concern I added a UPS to the Server and that cured that problem and they where so happy that I added another to the Burglar Alarm and stopped that going off all the time. That only left the Sunday morning triggering every summer that someone had to work out what was going on.

Col

First does this behavior happen only at night? Following the scenario you outlined? What happens if you try to power off first overnight then power on in the morning. If you do this a few nights and everything behaves normally then it maybe safe to assume there is some occurance with the AC going into the machine at night which can cause problems.The power supply will turn off the Power Good signal if a power surge or glitch causes it to malfunction.The signal will come back on when the power is GOOD again, this will reset the computer. If there is a brownout, where the lights go out for a split-second and the computer keeps running but suddenly resets itself, that is what happened. A Power supply may shut down and seem defective after a power problem but will reset if the power is turned off for a minute and then on. You could actually have a bad P/S or mainboard but check all power options in Bios first, make sure you have a surge protector and try as I suggested turning off the unit at night.