It sounds like the PSU is firing up and so I ex;pect that it is working alright.
It might be a good idea to try the motherboard outside of the case as you are going to have to dismantle it anyway.
The next thing is to remove the motherboard from the case and test it on the workbench.
Make sure that you observe anti-static precautions.Lay some cardboard or use the motherboard box that is non-conductive on the worktop and remove the motherboard/CPU/heatsink/fan/buzzer/one stick of memory/graphics card and PSU from the case and put it on the cardboard. Add the keyboard and mouse and try and boot. The system should try and make a beep or series of beeps. Please post what sounds it makes.
I can't speak for Gigabyte US but their office over here is very friendly. It usually depends on how you approach other people as to the response you get I find.