I have an almost exactly identical issue as yours with the Intel computer in my specs. The computer would certainly fail to restart, and it would hang at the Win 7 loading screen, followed by a BSOD which stated something like "An attempt to execute non-executable memory..." Memtest86+ for 10 passes turned up no errors. However, I noticed that when copying or downloading large files(1GB+), they would often get corrupted(can check this from the MD5 sums.) Programs would often turn up errors like "Reinstalling the program is recommended because so-and-so.dll has become corrupted" and zip files would turn up CRC-32 errors. I finally discovered it was the new 2 GB RAM I had installed few days ago that was the issue. Gonna RMA the RAM first thing tomorrow.
I really find it odd that Memtest86+'s reliability has been called into question... 10 passes and no memory errors...