I've seen SQL servers do this before and it has (as others suggested) been hardware. A memory fault which is only "discovered" as SQL starts to eat its way up through the new RAM (to its max setting). When first started it may only need about 2Gb, then as users hammer away it decides another 2Gb would be good and so on. Then it hits the fault and pukes.

Of course if you're running multiple instances and haven't limited the max RAM they can have... 😉