I doubt you would get it fixed for less than the cost of a new GPU but that would depend on what is wrong with it. They aren't exactly easy to fix. Even getting an estimate would likely cost a fair bit. One R9 290X or the new RX 480 would give better performance vs the 7990. The 480 would also be cheaper than a replacement 7990.
Depending on when you bought it, it may just still be under warranty with the manufacturer.
That's not good news
I've had it 2 years, and it was bought 2nd hand on fleabay, back when I still had some money, so no chance of a warranty claim.
I'm slowly drowning to death on £73/wk so buying anything new is an absolute no-no.
Think all I can do is sell the 7990 as 'not working', plus my video cams & hope I can get a used R9 280X in the auctions (min spec for Elite: Dangerous)
The only working GPU I have now is an old HD5870.