Could I send Nvidia a used video card to refurbish?
Bird Of Time
Can I send Nvidia an Apple Mac Pro Nvidia Quadro FX 5600 1.5GB Dual DVI video card to be refurbished, and how much would they charge?
NVIDIA doesn't make the cards. If it's even possible, you would be sending your card back to the manufacturer, of which there are many.
You should be able to find the manufacturer of the graphics board either on the board itself or through software, at which point you should contact the individual company that made the card.
Like drtweak pointed out, it may be better to just purchase a new card, as the cost of service is likely well beyond the point of diminished returns.