Err, my answer became the best solution without any solution. xD
Does the picture turn blank the moment windows loads? If you stay in the BIOS, does the picture eventually turn blank after one minute? If yes, then the motherboard is the culprit. If not, and the picture stays okay forever in the bios, then suspect a driver issue, or a bad resolution in windows.
If you are sure there is no issue with windows and the rest of the hardware, then your motherboard's on-board video seems the culprit. Unfortunately, there's almost no way of repairing onboard video cards, short of asking Gigabyte themselves. But:
One question: Does your pc seem to load correctly windows even though there is no picture? As in, does windows seem to work in the background and the HDD led flashes?
If yes, then the simplest solution to your issue would be to simply buy or borrow a video card and install it in the PCIE port. Even if the onboard video is defective, if you use a video card there will be no issues.
It is even advantageous for you, as it will make any games or 3D effect smoother or faster.