PC starting, fan spinning for a second before die

Hi, I have an old PC (maybe 6 or so years old with WinME license sticker on it!) that one day didn’t start anymore. I suspect the power supply is the culprit, so I decided to changed another one from my other DEAD PC.

That PC is now working for about 18 hours and died again with the same problem. What could be the REAL problem to this? I’ve scratches too much hair and want to avoid any more hair losing…

Thanks 🙂