I've seen a similar thing happen to a friend's laptop recently. After much toying with the battery, motherboard, and CPU, it did reach the POST, but then returned an error that, as far as I was able to tell, basically told me that it had an unidentified error with the motherboard. This was after the thing had gotten severely overheated.
Based on the fact that it's not even getting to the POST, it could be that it actually did fry itself due to a previous overheat or short circuit.
However, do follow any instructions that you can in the link about the POST that kimsland posted.
Try resetting the CMOS if you can.
Also, if there are 2 RAM sticks present in the computer, remove one, try to boot. If that doesn't work, swap them so the other is removed, try booting again. If it boots with one of them out, then that RAM stick might be the problem.
If you reset the CMOS and followed all the instructions in that link, then the motherboard and/or CPU might indeed be fried, and need replacement