I looked up your board at Newegg, and there are an inordinate number of complaints. I only went back to Feb 2015, but I am seeing way too many unhappy users and few fully satisfied users, I will just say that if the board is new check your return deadline and try no to go over it. Newegg has 30 days, not sure about Amazon.
Ok, let's go forward.
I will assume the following, please correct me if I am wrong:
> you say the the monitor tests good because you can use it on another machine and it works fine. So the video cable and monitor are good.
> when you boot, you get absolutely nothing on the monitor. Zero, not even the POST screen from the BIOS. No keyboard recognition system beep.
> you have checked that the video card you have is listed by Gigabyte as being compatible with that board.
Assuming the above is true, you have a low-level hardware failure. The signal from the power supply to the BIOS is not being received. This can only be caused by one of 4 things:
> The BIOS is corrupted or bad
> The power supply has failed
> The CPU has failed
> The motherboard is bad
Reset your CMOS back to factory default. The instructions will be in the manual that came with your computer. Try to boot.
The only way to check a power supply is either to purchase a tester, they run between $20-$50 on average, or change out the power supply with another you know is good. Realistically, it appears that your power supply is enabling the fans to spin up. If you have a power-on light on the board itself and it is lit, that is another indication that the board is getting power (that doesn't mean the board is good, just that there is electric signal from the PS). Does the power lamp on the board light up (assuming you have a power lamp)?
CPU...the only way to test a CPU is to swap it with another board, or a different CPU on the problem board. What you are experiencing is characteristic of a blown CPU: all the fans spin up, power light activates on the board, but no keyboard recognition beep, POST screen or monitor activity of any kind. Note that some of these newer monitors will post the manufacturer's name for a few seconds on boot, but that signal comes from the monitor itself, not the computer.
Motherboard: given the probability curve, motherboards fail far more than CPUs. The only question you might have is that you have a used CPU and only the vendor's word that it is good. That doesn't mean it isn't.
On the flipside, there are a lot of complaints from users' reviews on Newegg about that Gigabyte board. Hard decision.