Is this a known-genuine GTX960 or an "eBay special" which may or may not be an actual 960? Without model-specific drivers, the GPU gets initialized by Microsoft's generic VGA adapter drivers that will work on nearly any VGA graphics adapter from the past 30 years. GPU-specific drivers for acceleration however require that the hardware actually matches what the PCIe/BIOS info says it is so if the info got overwritten by an eBay scammer or similar, the drivers attempt to initialize the GPU following the declared model number code path and ends up in an invalid state because hardware does not match description.
If you are 100% certain the GPU is genuine, make sure AUX power is connected if needed, some GPUs will allow legacy boot without AUX but require it for hardware acceleration. Most either refuse to power-up or display an error message at boot telling you to power down and plug it in.
If none of the above works, the last ditch option would be to fresh-install Windows on a spare HDD/SSD and see if drivers still fail on that. If it does, then the GPU may very well be defective or otherwise bricked beyond basic VGA functionality.