Hi, I read a few threads about your motherboard. The only thing that came up was that Gigabyte recommends "non ecc un-buffered memory" and then it should support up to 16GB of RAM. Do you have a friend that you can borrow some RAM from to test it out?
On the Gigabyte website, check if you already have the latest BIOS. Often if you don't you can check in the firmware notes something like "Improved Memory compatibility" or something and then you know that it will probably fix your problem.
Normally you only have to install new firmware when you have issues, but since you do, you might want to take the risk. But the risk isn't big if you do it correctly. I myself have flashed countless firmware without problems. Avoid power failures and make sure you download the correct firmware for exactly the right revision of your mainboard. Was it this same type of motherboard you had to RMA?