As @phoebus points out it could be a number of different issues. Powersupply and heat issues are good guesses, but it really runs the gamut. Let's start with some easy troubleshooting.
- unplug your machine (ideally you'll have your machine grounded but not powered, but eh)
- Re-seat all of your motherboard, add-in card, and drive power cables. Re-seat all add-in cards and drive cables. (by re-seat I mean remove and add back in)
- check for non spinning fans, and clogged fans/heatsinks as @phoebus suggested (if found, you can usually use a q-tip or tweezers to clean them off) a clogged heatsink is useless.
- swap outlets
If that's not working, let's get to the basics:
- unplug your machine
- Disconnect all of your drives from your motherboard (we don't care about booting right now, we just want it to POST and stay on--hibernate is not the issue) I mean everything, HDDs, optical drives, floppy (if you have one), unplug it all from the motherboard.
- Also remove all of your add-in cards excepting your video card (if you have onboard video and an add-in card remove the add-in card).
- Remove all of your RAM except for 1 module and make sure that's in the primary slot (DDR1 or something silkscreened on the board).
- Unplug everything external from your computer except for power, monitor cable, and keyboard (really, everything else--mouse, USB things, audio--it makes life much easier).
You should now have a motherboard with processor(s), a stick of ram, a single videocard (onboard or separate).
There should only be power, monitor, and keyboard attached to the motherboard (and the power is unplugged).
Reset the CMOS, jumper or button, let it sit for a while. Now, remove your battery. Walk away, make some tea (remember power is unplugged for this). While your tea is brewing, have some cheese toast, you don't need this much time, but it will allow you to relax.
Now, check all your power connections
Pop the battery back in and plug it in, is it still doing the boot loop?
If not, unplug the computer, plug in the next item and retry.
Start with say, your sound card. If it stops working at any point, remove the last item, and continue on with the remaining items. If you get all the way to booting congrats something was loose somewhere.
If it is still doing the boot loop while you're at barebones...
- swap that stick of memory for another one (check to see if it's still a problem)
- now, at this point your fans should be clear, and your heatsinks look like new, right?
This is where you are left with few culprits. It could be your processor or motherboard (mostly unlikely), still a heat issue (most probable) or an issue with your powersupply (possible), or your video card (eh, maybe), short in the keyboard (I've seen it), short in the monitor cable (seen it), short in the power cable (this involves fires and melting, you should notice that). In order I would try the following:
- swap out power cable, keyboard, monitor (one at a time, in that order, because you have a bunch of power cables, and probably fewer of the other two)
- remove heatsink from processor, clean processor top and heatsink until your heatsink looks new. apply thermal paste (remember a very small amount). Cod liver cream, or zinc oxide sunscreen work for a very temporary, risky fix (not recommended). reseat everything careful here, if you've not done it before, read up and call a buddy, it's easy to snap things off of the heatsink, and forcing the CPU with ruin your day.
- swap out powersupply
- find someone willing to loan you their video card replace yours with it and try again
- find a buddy with a compatible motherboard and either try your chip in his board, or his chip in yours, try again.
- remove the motherboard from the case, and the powersupply, set it up on a hunk of plywood after wiping it down. shake the empty case out. run stuff from the plywood.
- proceed with percussive maintenence
- request additional help on superuser in this question
I've probably missed an obvious step, I'll check back tomorrow and see what the status is.