DId i mess up the battery or alternator

I have an Audi a6 avant quattro. I used this car to jump a dead battery on a 96 ford explorer. battery startyed aactin up on audi. Now the gauge says that my battery has full power but it wont turn over(start) battery gauge indicates fully charged but cant start. truns over as soon as I get a jump but wont start if I leave setting for a short time. can drive when I get a jump and all is fine untill i turn off car. Do I need a new battery or did I mess up the alternator???