I bought a new power supply yesterday, I installed it and the system has been stable since then.
I want to thank all the great people that commented here in the blog and emailed me with their suggestions. The faulty power supply was one of the most mentioned cause you suggested, one that I hadn´t considered.
Why did I take so long to fix it?
I discarded other possible causes in my free time, being the PSU and the motherboard the last two (the most expensive ones).
Now progress resumes, I´m preparing the tileset and backgrounds for the final area. It´s fairly small, I should have it done in a couple of days.
Thanks again for all of your support, and for taking the time to write. (Sorry if I couldn´t reply all the emails!)