Computer Overheats, Dosen't turn back on, CAPS Lock blinking once.

The answer is most likely a simple one, you ignored the overheating issue and now you have potentially turned your laptop into an expensive paper weight.

First of all open the laptop and clean it! Remove the heat sink and fan, clean all the vents and the fins if the fan, get some thermal paste, clean whatever is left there from the original paste and apply the new paste to the chips, and set it back up how it was.

Also try to boot the laptop without the hard drive and see if it boots, excessive heat can lead hard drives to fail quickly.

Will it power on, maybe. From a brief search online the one blinking light seems to indicate cpu failure. If that is the case provided the cpu isn't glued in place it should be cheap and easy to replace yourself. If you go through all that and it still will not work then the issue could be deeper, there could be damage to the board somewhere.

You could also try to reflow the gpu with a hot air gun but you are best narrowing down the issue before preparing for this one.

Good luck.