I had a very similar problem... I would be working on my computer when all of a sudden it would completly freeze up. I would restart it and would get the continuous POST beeps which means RAM problem. So I laid my computer down flat on it's side, so the motherboard was also laying down flat, and it would work until I moved it vertical again... it would just freeze up again. The post beeps indicated RAM problem, but I had a hunch it was the mobo, so I switched the mobo with a good one and it worked just fine...

Just thought I'd share my experience... Now that I think of it I could have tried cleaning the RAM slots out with compressed air first...