Check for GPU main IC. Is the critical part. In particular, check solder balls. sometimes, cards get twisted because of heat, or improper fan/heatsink installation. Also, mechacnical stress because of partial de soldering is absolutely deadly. Probably you will need some reference
I attached an image of my old videocard. It's clearly twisted and main IC is partially pulled up from the right. Thermal protections were defective and the heatsink was "meh" installed. compare with your card. Take a good photo of it, with a spatial reference(a ruler will suffice) and paste it in some software like autocad. then you can measure how much is twisted. If it's "too much" mm's, probably your card needs some resoldering, but nothing is guaranteed. First think about possible reasons to get the card to that state (bad installation, overheating because of abusive usage...).
If not, check the power stage. Sometimes, those mosfet or thyristor arrays get burnt. You will notice that in that zone, probably the card smells pretty bad there because an old overheating there. Normally this type of failures make protections cutoff "hot" (in the sense of high power) multiphase power stages, so is impossible to detect an overheating, or malfunction, because card is essentially turned off, or in a sort of stand by state. If you detect a "goddamn hot" zone and you have canned dry ice, shot some there and check if this can get card working. If this forced cooling works, try to identify who is getting hot. Measure if you can for ridiculously high currents, in other words, an unbalanced power phase, or just burnt.
Check for cracked power connectors, or solderings on those connectors, loose cables. A spare power supply can help also there.