Tom

Desktop computer, I've had some overheating issues for a while so it's probably damaged hardware.

No, it doesn't make any beeping noises.

If it doesn't make any beeping sound, then it's the processor. Also, you said the BIOS showed up right? It's indeed a component which gets overheated most. My old PC was in a very terrible condition and got problems with its processor very often. Try to clean it first, add some... thermalplast or whatever is the name, and turn it back on.

Silly method, but (almost) always worked in my cases.