I would not recomend you use the GPU. If you have the Capacitor, you can try a repair. Use a soldering iron and put some lead on each end. Be carefull not to put to much and make both end touch. Then place the GPU on a flat surface, place the capacitor and with some kind of instrument try to hold it in place. Like a needle on a stick, you just want to prevent the capacitor to fly away. Using a heat gun, heat the capacitor to make the extra lead melt and reglue on the board. You can try with the iron, but you could damage the pcb even more. You also risk to short the board.
However if the GPU is under warranty, I would contact them for a RMA. This could fall under warranty.
Once you have repair the GPU, cross your fingers and hope you don't blow up your mobo. if you have an old PC you don't really care about I would try the card in it 1st.
If you lost the capacitor, you could try to get a new one, but you will need to find it's charateristic. And I have no idea where you could have that info.