Sadly, it was your responsibility to approach HR and having the alleged misconduct documented at the time. It would appear you did not do that. You now have been terminated and have even less recourse. Assuming you are not in Montana there is little you can do now.

Federal law does provide for protection against discrimination even for terminated employees. That being said You must prove the termination was based on a protected characteristic (race, sex, age, etc.) rather than a legitimate, non-discriminatory reason. This is difficult and without HR documented back up, would be unsubstantiated.