Usually faulty RAM will generate a blue screen of death with something like cannot_page_in_nonpaged_area. "paged" and "non paged" in the error usually mean bad ram or hard drive.
If you really want to check your ram:
http://majorgeeks.com/MemTest_d350.htmlYou got like 4gb ram so need to get two of these going at once. Have one set to 2000mb and the other "all unused memory" and let them run till it gets over 100%. They will run until you tell it to stop.
http://majorgeeks.com/Video_Memory_Stress_Test__d5896.htmlThis needs to be done in regular mode and will test the memory in your video card.
I'm doubtful anything is bad. If I was working on your computer in the repair shop, would run memtest overnight and video stress test over lunch. These test will take quite a while, the video card one might take over an hour.