Should I appeal the F grade I received in my programming class?
Mistakes happen.  If the prof couldn't grade your work because of some system problem -- regardless of whose fault the problem was -- it could have easily been resolved at the time with a simple email from the prof to you.  You could have resolved the issue, and he could have deducted an appropriate amount for the glitch.

In the meantime, I assume that because you're using a version control system for managing the project, that absolutely everything is time stamped.

I think you'd be in line if you send one more polite email, once again apologizing for screwing up privilege on his access, and asking him to please reconsider the grade, given that all the submissions are time stamped, and that you wish he would have notified you of the problem when it arose, and not surprised you with an F.

If that doesn't work, you might politely approach the department chair.

It goes without saying that I offer this advise assuming that I know the whole story, and that there are no undiscovered surprises such as academic dishonesty anywhere in the mix.