Start fresh now that you've got a new BIOS. Make sure you cleared the CMOS after you installed the new BIOS. Then, using only *one* memory stick at a time, run memtest86+ for a couple of hours. If it works OK, swap in the other memory stick and run memtest86+ again. If that works OK, install *both* memory sticks at the same time and run memtest86+ again. If that works, your system should be stable.
I wouldn't trust your current installation of Windows, since you did it while the system was unstable, and BSODS could be caused by previous corruption of the Windows install. So, reinstall Windows. Then, run PRIME95, one copy per core, in the stresstest mode that stresses the CPU and some memory (I think that's the 2nd of 3 choices). Let that run for a few hours at least to see if you get any errors. If not, you should have a stable system.
BTW, what brand and model power supply are you using?