Engine cranking, but will not turn over
 

I have 1999 Audi A4 2.8 quattro. Whenever I try to start the car, the engine makes this extremely unhealthy hiccuping sound (try to imagine starting an old beater from the 1970's, it sounds just like that), and I have to keep the key turned for about 20 seconds before the engine 'sort of' starts up, and then I have to pump the gas pedal just to keep it running.

This is not a constant issue, however. On some occasions, the car starts right up no problem.

I've checked the battery, it's fine. I've heard it could be an ignition coil, the oxygen sensor, spark plugs, or the catalytic converter. But I really don't know what could be wrong with it. Any ideas?

One thing I'd check is the ECT sensor (engine coolant temp), especially if it's worse on cold start. You pretty much need a scanner hooked up AND have the symptom to do this. See what the temp is reading. I ran into a couple that would show (for example) 180*f cold. The ECM is fueling for a hot engine vs cold, and will act like a carbureted car with no choke. May want to monitor it from cold start to hot, it should increase steadily, not all herky-jerky. As long as the sensor reads in range it will not set a fault code or check engine light, even though it's reading wrong.

OR, they're cheap enough to change (and fail on a regular basis) maybe just change it and see what happens(?) If you do change it, be sure to get also a new o-ring and retaining clip along with it.