first, let's narrow things down. unplug ALL peripherals except the mouse, keyboard, monitor.
Also remove any internal PCI cards like audio etc.
Power up, reboot and see how it goes, then replace the items one by one until the system hangs.
Another thing if the above fails, it may be a memory problem (try removing and reseating the memory modules) or the internal cooling is not working, making the processor act funny. try opening it up and observing the fan on the cpu itself.