I dunno dude, depends how badly you damaged it...if it is completely broken off then most likely the circuit is cut and the mobo wont even boot up. If you just damaged the capacitor, ie, popped it then it may start up. Long story short, it isn't worth risking the fire....probably best just to get a new econo board for 100$
No it wont be covered under warranty. Capacitors are needed too keep the computer stable. While I know computers can run for a while with some failed capacitors generally it will cause failure of capacitors all around the board which can lead to hardware failures, but eventually the computer will stop booting.
If you have a really hot soldering Iron you should be able to remove the old cap and replace it. http://www.rs-components.com/index.html you may be able to find your capacitor their. I believe its most critical to match capacitance but it may be by ohms I don't really remember.
Same problem here, same Videocard, same capacitor, a Gigabyte motherboard. This GX2 is a pain to mount and unmount, my first one was defective so I pulled it like 10-15 times to make tests.
Did you fix your board? It is a 100 uf capacitor. Cap-Elect, polymer, 16v, surface mount, Radial. Found it at Digi-key, catalog number 565-3210-1-ND, minimum 5 pieces is the order, cut-tape packaging, runs for about 5 $ for all 5.