I have had customers have this happen on their machines as well, and it can be a number of different things.
1. Software related? Yes, it can be. but that is easy to test by doing a clean boot with all 3rd party apps disabled. This could also mean viruses as well, but since it is a new machine it is less likely.
2. Bad memory. Have had this happen as well, where the memory had bad spots that where at the higher end, so the problem didn't show itself until more memory was in use. Doing a memory test can confirm if it is the memory or not.
3. bad sectors on the hard drive. This happens a lot, system files or something hits a bad sector on the drive and the whole system locks. This is easy to test for as well.
4. Bad drivers, somehow one of the system drivers could have got messed up. (This doesnt happen very often, but it does happen)
So basically it is a process of elimination.
Shane