There's clearly an issue with the fan control circuit. It's just not clear what kind of an issue... Can you try setting the fan(s) to a fixed speed (regardless of load/temps)? I'm not suggesting that's a viable long-term solution, it's just to determine if the control logic is at fault or if the PWM signal generator is somehow defective.
If it turns out the card is able to keep a fixed fan speed, the PWM portion is fine, and it's the logic part that's somehow confused. You could use a 3rd party fan profile tool, like SpeedFan or even Afterburner (or some other vendor's OC/fan management) and make your own fan profile that will be controlled by the PC's CPU. It's a workaround but it should be better than giving up on the card.
If there is, in fact, something wrong with the PWM signal sent to the fans, then no amount of software will help you. Solving this would most likely involve soldering and replacing small SMD components, so if you're not comfortable with that, it's probably best sell the card as semi-defective and buy a new one...
Careful what you wish for... You just might get it.