So back from my trip, finished the backlog of work that came in, and can fiddle with these boards a bit more.
First up is an AMD R9/270 that I picked up on Ebay broken. Sure enough it didn't come up as a display, but was registered by the computer. So something was working, just not the whole thing.
The board
It's really pretty simple: On the left is the high power circuits for the GPU, on the right is a lower power circuit pair for the memory, and hotel circuits.
If you look more closely at the left side you can see how this is powered: Five separate chokes indicate 5 power supplies. The little FQDN chips next to the chokes are the FETs plus drivers plus dead-time logic. The lettering on them is hard to read but I can see they are Fairchild 6705B half bridge buck drivers. They contain the switching logic, a high and low side FET, and appropriate logic to determine cut-through and current sensing (via the little RC circuits at the bottom of the board). Pretty simple actually, according to the docs each one can handle 40a of current, so we're looking at a max of 200a into the GPU. About right.
The question is: What is happening? Normally the high side FET shorts, in which case the cut-through circuitry crowbars the low side and shuts down the controller. The problem with that is if +12 was connected to the GPU the low resistance of the GPU would essentially short out your powr supply or blow the GPU sky high. Given that neither are happening I'm not sure if the failure is in the FETs. It's possible the low side FET blew, but since the Rds switching time is mostly on for the low side in a buck converter they don't usually ever short out. Plus the voltage drop on the high side is much higher (going from 12v to 1 instead of 1v to 0) so the high side FET normally blows.
Hm.... One way to find a shorted supply is to pull the chokes and check the resistance of the circuit at the output/FET side of the choke. The bad supply will read high (or low if the low side FET is shorted) and you're in business. Or if the FETs are exposed you can look for a short between gate and source or drain. Normally when a FET blows the gate is shorted as well.
Need to think more about this.