When I turn on the computer, the Windows 8 loading screen appears, then it says there's no signal to the TV. It doesn't display any sort of error message or anything. The computer has a Rampage IV Gene motherboard, if you need the full list of specs I can add them to the post.
I have restarted the computer about 10 times, all exactly the same result.
I am able to get into the BIOS, but don't know if I can fix it from there.
It sounds like a simple resolution mis-match. Your HDTV is not able to display the resolution your computer is outputting. You can try to rectify this issue by booting into safe mode (is that even an option in Windows 8?) and if you get a desktop, try different resolutions until the highest one still displays.
Otherwise, what I usually have to do is connect the graphics card to a normal computer monitor and then connect the HDTV as a secondary monitor to find an acceptable resolution/refresh rate.