Okay, I already know what it was: the power supply.
It wasn't completely broken yet, but it was on its last legs... I went to a trusted store and they recommended putting a more powerful one in (520, if I remember correctly), I changed it and... ta-da! the problem disappeared, both the electrical noises and the temperature spikes and slowdowns... my PC is working properly again!
However, I got myself a UPS, just in case... I don't trust voltage spikes. And I'm also thinking about putting a cooling system on the CPU and the graphics card, which are the parts that suffer the most in my computer... I'll look into it when I have some money.
Many thanks to everyone for the help, suggestions and advice... now, if any of the administrators can close the thread, we can consider it solved, even though in the end it had nothing to do with the graphics card... 
That's it: Thank you very much!