My suggestion :
First of all check the small fuses on the video card, if one is open then you know that area has problem.
The card will take 12v from the pci-e slot and will take 12v from the extra pci-e 8pin power connectors... there's gonna be fuses for each.
The board has a vrm with multiple phases and it's quite possible that a few phases re powered from the pci-e slot, and the rest from the pci-e 8pin connectors - for example there may be a 8 phase vrm, and you have 2 phases powered from slot and 6 phases from pci-e 8 pin connectors.
I would suggest using a pci-e riser adapter like these:
https://www.amazon.com/dp/B075ZSDD4H/I don't mean exactly that one, there's others on eBay for much cheaper --- you just want one that takes in only 12v and has 3.3v regulator on the board with pci-e x16 slot - this way there's no power coming in from the PC, all the power is from the 12v cable.
So, you can connect the 12v input and use some pci-e 8pin cables to power the whole video card with 12v, and you can limit the current going to video card to something like 1A ... this would allow you to safely start the video card with no heatsink on it (maybe just a small heatsink on the gpu chip alone) and you can use your finger or some isopropyl alcohol drops to see which mosfets or regulators or ceramic capacitors heat up significantly - that could indicate a short.
If the mosfets in the VRM or memory regulator don't heat up, it could be they're not even starting because the controller is dead or a fuse is dead so electricity doesn't even reach that circuit.
0.5A or 1A should be fairly safe, as long as you pay attention ... a video card board is thick enough that a shorted mosfet will dissipate 10w or so easily into the board so it will last for a few seconds until you spot the burning hot chip