Unfortunately, I'm out of money for a new fan, so this one will have to do.
Anyway, I've managed to keep the computer running for several hours without any issue, the temp staying just below 60C most of the time, with highest reached of 70C and lowest of 54C. Made it run CPU-intensive programs while monitoring temps and fans. Would stay around 63-65C, no lag whatsoever, fan barely spinning once in a while when hitting 65C to cool down. Started doing my own business as usual, and again no problem detected, no over-heating, no lag, nothing.
However after a few hours of this, while playing a MIDI file, the freeze and the long continuous beep sound came, while CPU at 58C. Upon restarting, became laggy and unresponsive before Windows finished loading. I was able to bring up the task manager to check on processes. I noticed System Idle Process having a value of 00, implying some other processes would be eating up all ressources. However, all other processes also had a value of 00.
UPDATE: I just found a new defective hardware that could be partly or wholly causing the problem. My graphic card has 4 blown-up capacitors, 2 of which are leaking...