What mode is the SATA controller running in? You should see ATA, AHCI or RAID for your choices. If it is set to either AHCI or RAID, the 7 install DVD may contain an unstable driver, causing the system to bluescreen when using that controller mode? Also check to make sure your BIOS is up to date. I have seen out of date BIOS'es cause quirky issues like this.
Edit: Also run over to www.memtest.org and grab the latest Memtest86+ version (now at 4.00 I believe). Run a full pass on your ram to make sure it's not faulty, rather than swapping it into your other PC.