To work this out - now test the 1 gB module by itself. Let the test run for a minimum of 3 passes (if you get no errors)
If the stick passes in both slots - then the 2 gB stick is bad
If the stick fails in both slots - then it may e a bad motherboard, or that both sticks are bad.
In that case, either try new/other RAM that tests good in another system - or test your RAM in another system.
Finally, if the stick is good in one slot, but bad in the other - it's most likely that hte slot that it's bad in is also bad (so it'd be the 2 gB stick is bad and the motherboard is bad).
This isn't likely, but it covers all the bases with testing.
Good luck!
Once you remove the bad RAM (or bad motherboard) - should the problems still occur - then post back and we'll look at other things.