You're right that faulty memory can cause this STOP 0x00000050: PAGE_FAULT_IN_NONPAGED_AREA error.
Since the system works with just the two new sticks of RAM inserted then it seems likely this is the cause. RAM has to be compatible to the motherboard and to any existing RAM sticks to work correctly and if the new sticks don't match the old sticks this can cause the error.
More on 0x50 here - http://aumha.org/a/stop.htm Click on the "50" link in the left hand column for more details.
Try Crucial.com's Memory Advisor Tool at http://www.crucial.com/index.aspx and they will tell you exactly what memory this system can take, and what type.
Other than that, the Aumha site suggests other possibilities, such as "incompatible software (including remote control and antivirus software)"
That's a start.
Mark
I have a Dell Precision 380 running XP Pro. In the past couple of weeks from time to time I have been getting the Blue Screen of Death. The error is OX-50. This seems to happen more when my daughter is playing games. I looked around online and found what may be the solution, the video card and or the memory. My video card is ATI firegl V 3100, I updated the drivers and the BIOS. I have 2-512 mb of memory and four slots. Earlier this year I bought 2 extra 512 memory sticks. So I replaced my old memory with the new ones and everything works fine. When I put all 4 memory sticks so I can get 2 GB I get an error message X300 Pro 128mb Bios P/N 113-A33405-100. How do I get the computer to see all the memory? Can memory cause the Blue Screen of Death? Here's one other thing it seems it's taking longer to load all the desktop icons. Thanks!

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic