It should be fairly simple - if you bought it new from a reputable dealer and it's in warranty then Gigabyte or their partner must fix it, unless the reason for the problem can be attributed exclusively to the end user. Somehow, I don't think a capacitor falling out or not present at purchase is your fault....sounds like a manufacturing issue.
Possible. Sounds to me more like a card that someone needed parts from, or has tampered with and returned as a bad card, then it got repackaged to sell. This is not uncommon at all, I have even seen people abuse retailers return polices to the point that most simply won't accept returns any more because so many idiots do try to take advantage of the policy.
I have seen posts like " just buy 2 or 3 on your credit card, use them for a few days, and return the ones you don't like, they have a no questions ask return policy......." or "just buy a new one, take the heat sink and fan out that you need, put your old non-working one back on, and return it saying it doesn't work"
So they ruin it for the rest of us.
Gigabyte is a very reputable company and they would do some type of exchange or repair unless they had a good reason not to do it.