Alienware Aurora freezing issue w/Razer mouse & keyboard shutting down

I have an Alienware Aurora that I've had about a year and a half.  A couple months ago (just after the warranty expired of course), the computer started have screen freezes and when this happened, the Razer mouse and keyboard that I have hooked up to it would stop responding and the lights would turn off.  I got so frustrated with it, that I swapped to my laptop and I came back to the desktop today to see what I could do with it.  I opened it up and reseated the RAM, cleaned out any dust and changed the clock in the BIOS to get rid of the pesky beep that it had developed on startup.  I ran the PSA diagnostic and it came up with a memory fail somewhere during the test.  It didn't give me an error code, so I can't figure out what it is.  It was on this string: Testing 01_00000000h - 01_BFIFFFFFh (3058 MB) with 8 CPUs.  Not having any idea what that was, I reseated the RAM again and then ran the Windows 7 integrated diagnostic, a full one and it came up clean.  I also just ran the Dell diagnostic from the website and it came up clean.  I'm now updating drivers.  Since I reseated the RAM for a second time, it hasn't given me any issues yet, but it's only been about 45 minutes.  Anyone have any ideas on what this might be?  I'd rather not go through testing each stick of RAM individually if I don't have to.  Thanks in advance!