Just trying to put mind in gear.
Except you seem to have hit the reverse
Try not to post information you're not positive on, ok? Let's not pollute the forum any more than it already is.
OP, a good 750W PSU should be considered a minimum for mining with those three cards.
The 7970 itself can chew up
250 W. The 4870 is not exactly power efficient, neither is the Bulldozer CPU.
A 1000W unit would be a prudent choice if you want some flexibility with the cards - the
Kingwin Lazer Platinum 1000W is 80+ Platinum certified (you can't get a more energy efficient unit) and can be had for
about $180.
I take it that's not a dedicated mining rig, is it?
If it is, you should disable four cores in the BIOS as you won't be using them anyway.
Using just one GPU (e.g. the 7970) run the
OCCT tool and upload the graphs it creates, that will shed some light on the voltages and thermals.
Start with a 30-minute CPU test. If the machine doesn't crash, try the GPU test. Re-try those tests for a prolonged time (like an hour).
If the machine is still stable, try the PSU test (it runs the CPU and GPU tests combined). An inadequate PSU will surely fail here.