OS is causing memory issues?

So, I'm working with a friend on troubleshooting a mid-range machine that he put together, and we've hit on an issue with the memory that we just can't figure out.

Specs of the machine:

• AMD Llano A6-3650 CPU/GPU chip
• Biostar A75MG mobo, originally an ASRock A75M
• Kingston HyperX DDR3 memory, 4GB x2
• Antec 430W PSU
• WD SATA HD, Samsung optical

So, the trouble began when the machine wouldn't even POST. Bad motherboard, we though. So we swapped to the Biostar board as above. Machine POSTed, OS began booting.

At this point, Windows 7 started having some serious stability issues. Machine would either bluescreen while booting, or get into the OS only to bluescreen out shortly after, or get into the OS only to have programs start rampantly crashing with memory errors. In this time, we managed to get Open Hardware Monitor running, and did some rudimentary stress testing with Prime95 before they both crashed out, nothing hotter than 55 degrees C or so. Sounds like some bad memory, so we ran Memtest86+ against it. Sure enough, errors galore - tens of thousands of them.

We began trying to narrow down which memory stick was bad, if not both of them. Testing each stick individually yielded no errors. Huh. The motherboard has two memory slots, so maybe one of those was bad. Testing each stick individually in the alternate memory slot yielded no errors. Huh. So we put both sticks back in, in the same configuration as before, which yielded... no errors. Huh. This is after multiple memtest sweeps each, for each round of testing we did.

Here's the part we can't figure out. We went to boot again, and encountered the same instability. Went back to memtest; errors galore again. What!

We went to check the voltages on the various parts of the system, on the off chance that something is being under/overvolted; everything was coming up normally.

tl;dr as far as we can tell, loading the OS is causing the memory to go bad

Have we missed something here? Since when does loading an OS cause memory errors to appear? Please help, and thanks in advance!