So, I recently acquired a 1985 Audi 4000s Quattro. When I first got it there were some intermittent starting problems, but they were far and few and I attributed them to the bad alternator/battery. So fast forward, now all that's replaced, volts are good finally, and the car is great for a few days. Then it begins to refuse to start more frequently, but the starter and solenoid are also new and the headlights go off when I turn the key. It now starts very rarely. I took a test lamp to the connections going to the solenoid. It turns out it is only getting power when I turn the key once out of maybe every 30 times. Does anyone have any idea what it could be? The headlights dim when they key is turned, but could it still be the ignition switch? Im stumped and kind of discouraged

 

I'd bet all my chips that its the ignition switch. The EXACT same thing happened to my Altima. I know its not an Audi, but your symptoms describe my problem to a T. I just pulled the trim from around my steering wheel and figured out what wires to cross to make it start. Then i just spliced a wire in to bypass the faulty switch. The car starts normally and you'd never know the switch was bad unless you pulled that trim off.

my 2 cents.

Good luck!