Gigabyte? No this info is probably available for the respective CPU (Intel or AMD) manufacturer but you never mentioned what processor it is. Such information is usually in a datasheet. Edit: I did a brief search and didn't find the datasheet so apparently this info isn't as popular as it used to be, so my next paragraph is less relevant unless you manage to find the FM2+ pinout.
You'd flip the CPU over, compare what pin is damaged to the datasheet diagram which is going to call it something like A23 and then a table that lists each respective pin name and function.
Since CPUs have more pins devoted to power and ground than each signal, odds are more likely a broken pin just reduces the max power (vs temperature) stability but often which motherboard is chosen (the quality of the VRM subcircuit) matters as much.
I don't mean to imply it couldn't be a pin with a more important singular function, but ultimately there is not much worth learning and doing with it if it tests stable. It's kind of like jumping into the middle of the learning curve but with no way up because such things aren't repaired except by replacement, like with automotive repair you don't weld in a new bearing and o-ring to the existing housing when a water pump fails.
In other words, both in automotive and computer repair, they are integrated to the point where certain things make sense to repair at the most discreet low level possible and some don't, instead take more labor than it's worth.
This is also applicable to automotive repair. I can't tell you how many times I've reversed engineered faulty circuits on vehicles, told people to desolder and replace transistor X instead of buying a whole new fan motor controller, or resoldered a cracked joint on a vehicle temperature sensor display, or hacked a lamp out module when someone wanted to put LED lights in where incandescent were the factory lights but then ended up with a dash warning them their lights didn't work due to lower current consumption.
There is a certain satisfaction at getting to the core problem and fixing it quicker or cheaper, but in recent years the supply lines and retail presence for components, whether consumer computer or automotive, have reduced the replacement costs and thus the value of the time to become an expert on such things to repair them at a discreet sub-component level, unless you have too much free time.