If you know someone with the skills it seems a shame to bin it without even trying especially considering how cheap that part is. Just need to find someone who can give you a definitive answer as to exactly what it is. I discounted it being a coil due to their being a coil of that rating just to the right.
After some sleep and more googling the internet seems to concur it's an inductor and that they tend to blow. A few almost identical pic's to yours. Apparently that whole area was cheaped out on and furmark likes to kill them.
https://www.google.co.uk/webhp?hl=en...n+1r0+inductor
If it just died of old age/heavy use I'd say a fix would likely work, but it could of been blown by a problem somewhere else in the card in which case replacing it will get you nothing but a puff of white smoke.
Given it's such a high end card and apparently a common problem shooting an email to gigabyte might be worth a go. Also are you sure it's out of warranty? even if it was bought at launch it would be just under 4 years old and their standard warranty is 3 years. Email:
returns@gbt-tech.co.uk