Thanks for your advice. I invested in a Corsair 750W modular power supply and connected it all up.
The fans started, the PC booted and loaded Windows. Everything seemed ok for a few minutes, then it restarted and hung when it got to the BIOS screen.
I switched the power off and booted it up again. This time it loaded Windows, so I tried updating the graphics drivers to the latest version and loaded the latest motherboard BIOS from the Gigabyte UK website.
I then loaded World of Warcraft and within a couple of minutes, the PC froze again.
Any ideas what else I should try?