A STOP 0x124 error is a hardware error - reported to Windows by your CPU.
As such it doesn't show any specifics about the error.
You either have broken hardware - or incompatible hardware/software/drivers
I say that corrupted drivers can cause this - but not all analysts agree with me on that.
The only clues were in your dump files - and that was the age of your chipset drivers (which weren't that old, but they were the only thing that I could find fault with).
So, unfortunately, you're at the point where someone's going to have to rip the computer apart. If you aren't up to it, then you're going to have to find someone who's capable of doing it.