To be blunt, NO, there is almost NO chance that your videocard could be repaired. I worked as an electronics technician for more than 30 years (I'm retired now), and even with all that experience, without specialized equipment and a swimming pool full of money, I couldn't hope to repair a modern videocard. The circuit boards have multiple layers, like a wedding cake, and repairing sub-surface damage (as an example) is impossible. There was a time when such repairs WERE fairly simple for a skilled technician, but the switch to BGA (Ball-Grid Array) mounted chips put an end to garage workbench repairs.
Sorry to say, if your card is dying / defective / dead, you can keep it as a souvenir or send it to an e-waste recycling facility. I have a few cards and old hard drives that I keep and use as paperweights, but I recycle everything else to keep it out of the landfill. The labor costs for repairing most modern videocards would far exceed the cost of a new card.
As an analogy, think about this: you can buy a new car (in the US) from a dealer for less than twenty thousand dollars, but if you bought each part individually and could somehow build the car yourself (assembling the engine, welding the body, painting it), it would probably cost you more than $100,000, with NO warranty and NO technical support if something went wrong. Many modern computer components are solid-state devices, simply etched silicon (or some other material) that has to be developed in a sterile environment, not something you could put together in your backyard.
Not trying to discourage you, but although I can repair most monitor problems or damage, I simply don't imagine you could afford the specialized equipment for repairing videocards, unless you have a swimming pool overflowing with cash.
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