S.M.A.R.T. directly shows the results of your HDD health, so give HDTune (or other HDD testing tools) another try to look for bad sectors.
If it's really bad sectors you'd get errors copying stuff up to the point it won't even detect in the BIOS. I know because it happened last month to me. :|
As for PSU, you'd need a PSU-tester to check for errors. I doubt it's the PSU though unless you always crash under heavy load.
edit: make sure all your cables are connected properly.
