It sounds like something isn’t set up correctly with your Git installation or the creation of your local Git repository. The error being returned is from Git itself, not from Toad.
As a quick test, I would try copying the local repository folder from the first PC which works to the second PC just to see if that fixes the problem. If that doesn’t work, I’d try reinstalling Git on the second PC. I’d also recommend checking Google. It seems other people have had similar errors under specific circumstances, for example:
There was an issue with Toad 12.8 and Git which caused numerous queries to Git for the config’s user name. This has been fixed in the 12.9 beta. I’d suggest giving the latest beta a try. Much of the engine within Team Coding has been rewritten, so it should perform much faster.
Have you signed up as a beta user yet? If not, you can register as a beta user and download the beta here: