By random I assume you mean that it doesn't freeze up in the same place every time. These are tough to troubleshoot but the most likely causes are bad memory, a bad I/O device, or an outdated driver.
It never hurts to have current drivers so I'drecommend updating everything first.
A cheap and quick way to isolate a bad device is to unhook every device except keyboard and monitor, (you should pull the cards for modems and soundcards). If your problem goes away try hooking devices back up, one at a time, until the problem reoccurs.
If you suspect memory you should be able to pick some memory cards at a local PC shop with a return policy. If swapping new for old doesn't resolve it then return the memory.
After that your probably looking at a motherboard or overheating problem.
Hope this helps. ..george