"..and the interval between the re-bootup and the freezing becomes shorter each time, to an extend that not even the motherboard's welcoming screen shows up..."
He can't get to the BIOS so how is he meant to get into Windows to use speedfan.
Again, like I said, test each part one at a time to narrow down the cause.
As the interval is just increasing, does it decrease if you leave the computer for a little while? If so, heat could be the cause (like stated above).
Graphics card could be another cause like stated above. Do you hear your computing booting up? (ie. Lots of harddrive reading etc) If so, your HDD probably isn't the cause.
I don't think it is the CPU as it should/would be more catastrophic. The computer would work one day and the next it wouldn't.
Motherboards are more unpredictable with many more parts etc.
RAM is somewhat unpredictable so a simple replacement test should tell you if it is the RAM, though I don't think the symptoms match up.
I originally said no to the idea of the power supply being the problem, I think if it wasn't providing enough power then the graphics card might display weird things, could freeze with not enough power to the CPU etc. If you have another computer with strong enough power supply to support the graphics card, do a replacement test with that to check.
Curious, did you install any of these parts recently? Also, I have had problems with stock overclocked (as in bought being overclocked) cards but obviously, if this part is a couple of months old, then that won't be the problem.