or just turn off hibernate, I have had issues with hibernate for over 8 years, and disable it on every computer other than laptops.
also most bios's have an advanced option to turn the S.M.A.R.T. testing on which will warn you during boot if the drive has problems, and also windows 7 & possibly vista also check the S.M.A.R.T. periodically and advice the user to back everything up if the S.M.A.R.T. reports an error.
as far as faulty ram, the usual symptoms are wrong memory size, will not boot, or intermittent problems, the last can be helped by switching the computer off & opening the case, finding the ram stick(s), un-clipping them and re-installing (ie push them back in to the ram slots).
and a third possible cause of problems is the video card, but it is a bit simpler to test ie do a windows performance test if the system crashes/locks up in the directx parts of the test ( the lock up usually will have vertical stripes on the screen) then the video card is a culprit
another possible cause of problems in computers is 'DUST BUILDUP ON HEATSINKS', the quick test for this is to shile a strong light at the heatsink while the fan is spinning, if you can see the metal of the heatsink behind the spinning fan then this is not the cause, if you do not see the metal heatsink then dust buildup will be making everything hotter than desired, and the quick fix is to shut the computer down and use a tiny artists paintbrush (about the size of a pencil/pen) brush the entire top of the heatsink so that you can see it through the fan blades
next on the suspects list is the OLD faithful POWER SUPPLY, if the case of the power supply feels significantly hotter than the air temp, then it is probably nearing it's limits(either of capacity or life) OR you see a puff of smoke coming from something in the computer, replace the power supply if the smoke has been released then it is too late you will have to replace the computer.
hope this helps
harpo