Hi and welcome to the Gigabyte Forum.
Firstly I would try a different keyboard. Normally I would advise a PS2 one but as you are already trying to use that try a USB one instead. It could be a faulty keyboard or controller.
If that fails to help then I would suggest building the basic system outside of the case on the worktop. Follow these instructions please.
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 and PSU from the case and put it on the cardboard. Add the keyboard and now I know you haven't got any graphics but try and boot. The system should try and then fail emitting a series of beeps. Please post what sounds it makes.
I originally tried a USB keyboard, found it disabled by default in the BIOS from the manual, and then tried my keyboard (PS/2). I know my PS/2 keyboard works as I've used it on both my PC and my wife/son's older EVGA Mobo based PC. The USB keyboard is working as I've tested it on my PC and my laptop.
I did some additional testing after I posted the problem on the forums. With my PS/2 keyboard connected if I spam the TAB key before the graphical post screen I'm able to get it to show the partial post in text mode. The Award BIOS label shows at the top with the graphic Award logo, and then the following string is below it "GA-EP43-UD3L F9". The post process stops there. Spamming the other keys (DEL, F9, F1, F12, END) before the graphical post screen has no effect still. I tried booting the PC with the HD, DVD Burner, and the case's SATA connections removed with no change. I unplugged the video card's power cable, booted up the PC and it gave me a single, long, consistent beep tone.
As for the building the PC outside of the case on cardboard, you mentioned a buzzer. I don't have a buzzer. Also, how would I initiate a boot up or shutdown without the case's power switch mechanism? Please forgive my ignorance/lack of knowledge.
Lastly, I think it would be poor thinking to design a motherboard with so many USB connections and yet have USB keyboard and mouse disabled by default in the BIOS. Even with that design choice it would be smart to put a warning label on the box and in the description that at a minimum a PS/2 keyboard is needed for the initial configuration of the motherboard. I would even go as far as to say that GIGABYTE should have included USB to PS/2 adapter(s) in the retail package. I would have paid an extra $5 to $10 US if they were included.