are you talking about a Live disk here? my reasoning being If you can run linux from a live CD but not from the HDD then this would point to the HDD being the problem,
what you could try is a complete Re-Partitioning/format of the hard disk using the install routine of the Live CD
Well I had actually typed that while I was starting the computer, and it seemed to work fine, but now it's dying the exact same whether I start it normally, with the Live CD, or into BIOS. So nothing's really working
It looks like a replacement motherboard may be the best way forward
reasoning here is if you could locate the faulty component you would then have to source and replace it and that is not really something for the average user. Modern circuit board production techniques do not make component replacement easy. A product of the throwaway society I'm afraid
if you can source an exact replacement motherboard within your budget then the only thing I would say is be sure that it is an exact replacement down to revision level if possible. Slight changes in components and connectors during a products life can cause problems when matching to cases and other components.