Check the capacitors near the CPU and the capacitors on the GPU, they should not be bulging, leaking, exploded, or otherwise trashed.
Pull the PSU out and peer through the grill and see if you can see the tops of those capacitors, too.
It sounds PSUish to me. Could be GPUs. You could take one GPU out, see if the problem still happens, swap GPUs and see if it still happens. If it happens with either GPU, it ain't the GPUs.
If it only happens with one GPU, doublecheck, and if it continues to be true you've found your culprit.
Check all the PSU connectors at both ends too, make sure they're all the way seated and are not melted/fried/hate life.