Car will back up on flat surface, but will not on an incline/up hill.
Reverse up hill on 2001 Audi A6 Quattro
If this an an automatic transmission , be sure you aren't just low on fluid. They act just as you describe when low enough.....
Is this Audi a stick shift or an automatic? If it is an automatic, it sounds like your reverse gear clutch is slipping in side your auto trans and this means work is needed on your trans ( not cheap). If it is a manual trans, then you most likely have a slipping clutch, which, needs service i.e. a new clutch.