Well good luck and please let us know how you get on.
An update:
I replied to the PM I was sent on the 8th, giving the information I was asked for and asking a few more questions. But so far I have had no response back, and still no RMA number. Frankly I think ignoring your customers for 2+ days to a direct question is unacceptable.
It looks like I will have to try and buy a new board and throw this piece of junk away. It'll be the last time I buy a Gigabyte product though - I am disappointed that a high-end brand like this shies away from its responsibilities over a small slip of paper. I have RMA'ed goods to many other companies over the years without receipts (AMD, WD, Asus to name a few), and it's never been an issue providing I can demonstrate that the item hasn't been physically damaged etc. I even have the box etc with matching serial numbers & the documentation etc to show I didn't just find this at the tip or steal a PC from someone.
It's a shame, I liked your products as I found the features, general reliability and price were well balanced. But if you take warranty out of the equation it just isn't worth the risk. And as I am forced to move house repeatedly for work, little things like receipts get lost, so I can't guarantee I'll always know where they are. Which is one of the reasons I went with Gigabyte in the first place - I thought with a warranty based on manufacture date I would be relatively safe. But it turns out I am worse off than if I went with a competitor.
You just lost a customer.