I had a similar thing recently where it would keep restarting, it got to different points each time before turning itself off. I too checked for virus's etc. but was stumped. I eventually put it in a local shop that I have used before and I know are very good (and cheap). He checked it out and said that it was the memory slipping. I would need a new memory, the only one available was twice the one I had in (my computer is only a couple of years old!) and would make my computer faster. I tentatively asked the price (thinking at least 100 pounds) It cost 40 quid fitted!!!!
I picked up the computer a couple of hours later, he even gave me the old memory stick. Never had any problems since.
The only drawback was that I lost everything on the hard drive and had to start afresh with all my settings etc. Taught me to back everything up in future!!