I have made a system with a 770T-UD3 rev 1.5 for a friend 2 months ago.
He wanted a PII X4 980 BE as CPU.
After i asambled the system it would not boot.
Although in the supported CPU list the 980 BE is not present the board booted just fine after i ve flashed the BIOS to the latest version ,the only one available on the site.
Also in the past i was able to boot a K9A2 Platinum with a X3 720 ,with a BIOS intended for Phenom 1.
It s about luck ,but i think you have more than 65% chances to work.
So flash with the 720 BE to the latest BIOS and try your luck.
I have latest bios too(F10, with no cores unlock present)... I guess its normal for 980 to suit on this mobo, an AM3 cpu use to suit on an AM3 motherboard, right? Has ever happened something different, in any platform?
So, why only 65%? I think its 95%
I said more than 65 %
I would get a 975/980 BE instead of that CPU as the unlocking to 6 core is based on luck,either due to the motherboard or due ti the CPU.
If you really want a six core get one from the supported list.
If a X 4 suffice for what you are doing get one of the ones i proposed as they are good performers and they work with that mobo.
An AM3 CPU will work in a AM3 mobo of course ,but proper BIOS is needed as well as proper hardware TDP support.
Ask Gigabyte for a custom BIOS if needed ,they should be able to do it for you in case it is needed.
Anyway buy the CPU and if it doesnt work return it to the store ,as this should be allowed having in mind you live in a UE country.
Edit: If that PSU is 450 real Watt it will work even with a 125 W TDP CPU .TDP specified is only a theoretical limit ,the CPU -s having usually lower TDP -s in usage than the one specified and thus sucking less power.Easy Saver software from Gigabyte shows the power consumption of the CPU in real time if you need to check out.