Random BSOD, freeze, reboot, boot loop, no minidump anymore.

Try to update your nVidia drivers.
Can you try to switch SATA cables?

Swapping SATA cables and switching them to other empty slots fixed the safemode BSOD! Thanks a lot Laith! I never thought of that!
Other problems are still there though, and new Nvidia drivers don't fix them; and as I said, most videos crash the display drivers if I have current ones.
Still no firewall/aero, no sound card detected, I guess I'll just reinstall Windows for that.
Still some BSOD and freezes but the PC is totally usable.
I might try to memtest the new memory stick as well to see if there really was a faulty slot, because I wish to buy another 2Gb stick to match the new one, but that would be sad if one of the slot really is faulty, and a 4gb stick costs like 100€ while 2Gb is 24€. And my 32bit can't detect more than 3,25 Gb.

I attached newest minidumps if that can help.
Thanks again, you saved me a lot of time!

Don't use 2 different sticks of RAM, use one model of RAM. Do run MemTest86+.