Not nessecarily. You said when you unpacked a large rar file it would restart, well, that taxes everything, but it uses 100% of the processor when doing that, now I don't think your processor is the problem, but rather the psu. It can't supply the power needed, and your pc restarts under load, and randomly when it really isn't under alot of load. Since it took 3 times to start up(with no beeps..), i'm thinking your HD or psu, I think most likely it is the the psu, but test out your hd with the tools first if you are able to keep it booting.
Also a bad psu can make your hd not show up or have errors as well, so even if your hd does show problems in a test, it may not be the root cause.
