Last week I put together a machine for a friend that got the parts for it.
It was an ASUS 7870, but mind you, after I installed the latest drivers, it crashed as well. Not a single BIOS modification, simply installing drivers, and GPU tweak (didn't mod anything)
The problem was that I installed the latest BETA driver. I had to solve the issue by safe mode deleting the driver and then use the 13.1 drivers.
Maybe that's what happened to you.
Well that sucks, I cant really help you that much.
I assume the build is new, right? Maybe if that's the case, installing the drivers makes the card stretch its legs with power consumption and your PSU of choice cant keep up. But really, im guessing here. Wait for further responses.