Hi again.
I think I've found the source of my problems, but I want to share it with you just to see if there's another possibility. As Lsdmeasap is away for a few days, anyone who has an opinion just post it, please.

After making all kind of tests, changing components and settings, I had reduced the possible cause of the problems to the motherboard and the CPU.
Today, I've finally had the chance to try with another CPU, an E2160.
The result, all the problems have disappeared, at stock speeds with everything in auto in the BIOS except DRAM main timings and voltage, which I set manually to my memory values, as the SPD values are safer.

I know it's an older (65nm) CPU than my E5200 (45nm), and it uses a different voltage, but I tried a lot of different manual voltages for the E5200 between 1.25V and 1.40V, without a difference.

So what I'm going to do is go to my shop to try to change the CPU, although I don't know if they will change it without testing it. It isn't as evident as if the computer didn't start or something. I even had Prime95 running for 3 hours without any error.
Anyway, I'll have to convince them it's faulty.

I would also like to know if it's still possible that the CPU is fine. I don't think so, but you never know...

Thanks for all the help in this forum. It has been really useful, I wouldn't have known how to start testing without all the information here.