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The back of one of my GPUs looked like this after a capacitor randomly fired a stream of sparks at me and burst into flames.

Did you try just replacing the cap?

I wouldn't know what value cap to replace it with, what would you suggest? It's a HIS HD5830 if that makes any difference.

It looks like that you will have to buy a new one Sad

That sucks, is it still under RMA?