Yes, you can connect directly to the PSU, but it you cannot view/control fan speed with that method. If connect through PSU, you do not need to connect to video card. But it is possible that the fan power connector on your video card is not working.
Does your video card have a power connector? I searched and saw some models have it and others don't. If it has one, did you reconnect it.
Does your video card have a power connector? I searched and saw some models have it and others don't. If it has one, did you reconnect it.