We just bought a 1985 Audi 5000 and we can't seem to get it to start. The starter for some reason won't turn over. We think it might be a problem in the neutral safety switch (its an automatic.) but we don't really know anything about that. We turn the key on and crossed the terminals on the starter selinoid and the starter turns but won't turn over the engine. I've heard that Audi's won't start unless it has a fully charged battery so that may be the problem, but it is charged enough to make all the lights in the dash light up and radio work so I'm not sure if thats true or not. I've never had an Audi so I'm kind of lost, we collect VW's so I thought it would be similar. So what could be going on here? Any ideas would be appreciated.

Oh wow! My dad had a 1985 5000 S, granite gray. One thing they were notorious from failing was the fuse box. It had a recall back then. It was some about corrosion that made the car run all messed up. Like inop AC and power windows.

Is located by the driver side on the bottom of the windshield. Take a look just in case.

A battery that operates the radio and some accessories does not mean that is fully charge. You need a load test for that. The battery is located underneath the back seat by the right side of the vehicle. Take 2 screws from the seat an pull it out. Need to jump? Use the red post that is located at the engine compartment.
On those models were wrongly accused of taking off on their own. My dad's car never did. The problem was the brake and gas pedals were close to reduce the reaction time. Some folks, were too stupid to press both pedals during braking. Therefore, the more you press on the brake the more gas you press. Audi came with a fix for that and was to replace the brake pedal with one that it was shifted to the right and a locking solenoid on the shifter that made you press the brake to unlock the shifter from P to R or D, like VW Beetle does. Check that switch too.

By the way, the New Beetle has the same Slanted Inline 5 engine... is a fun to drive with a TripTronic ;-)

Based on the information I'm picking up in your question, the starter turns when jumped but the motor doesn't turn over, yes?
If your connections are on the correct starter terminals, the short answer is that the starter solenoid is bad. Which usually, but not always, requires you to replace the starter.
Is the solenoid attached to the starter, or remotely mounted(is the starter perfectly round, or does it have a component piggybacked on it?)
The solenoid kicks out the starter gear to engage the pinion into the ring gear to turn over the motor. If the solenoid doesn't work, the starter will turn without turning the motor.
If the solenoid is out, the car won't start with the keyswitch.

i agree with ken you need a new starter, but the solenoid is actually a relay it receives a large among of power from the battery and a small amount from the ignition switch (because the ignition switch cant Handel the amount of electricity needed to turn the engine) if the solenoid is bad that would explain why the ignition switch wont turn the starter te reason that the starter wont turn the engine once you bypass the solenoid could be a few different things it could be that the starter is not kicking out to engage the engine in which case the starter will just spin continuously without kicking out (this would be fixed by a new starter) the second option that comes to mind is that the starter starts to spin then engages the engine and is stopped when it engages the engine this would mean you have a more serious engine problem (possibly seized). if the starter is simply not engaging the engine you probably just need a new starter which should come with the new solenoid attached fixing both problems the starter should turn when you turn the ignition switch and the starter should engage the engine turning the engine. (then its just a matter of wether the engine will start once its turned over)

the 5000 is a nice car you should enjoy it a good resource is audiworld forums there are alot of ppl on there that are always willing to help and advise on projects like these and its a good source for used and discount parts as well.