Thermal interface material
Cheap thermal interface material has a tendency to dry out and become ineffective after several years.
Remove the GPU from the computer. On the back of it, there should be two or more pushpins. Push these together and then inwards to loosen the heatsink from the GPU. Clean off the paste off both the heatsink and the chip that you uncovered using isopropyl (rubbing) alcohol, then apply a small amount (about this much) thermal paste to the top of the chip (don't spread it), then push the heatsink back into place. Make sure all the push pins are fully seated, then put the card back in the computer and see if it works.