Audi A4 starts some times and then won't

Could be your starter solenoid starting to go or a bad relay. Test all fuses and relays. Test relays for control and resistance. If these are good do the spark and fuel test to narrow your diagnosis. You have an intermittent issue so one time you might get a passing test the next not. Keep track of conditions when it starts and does not. Weather, overnight, hot engine, cold engine....

when you say " doesn't start " state weather it turns over or not or if it clicks ,, make sure the batt. terminals are clean and tight , don't let a vehicle sit for more than a week without warming it up if you can avoid it

A brief and quick question here is when you try to start the car is it in direct sunlight on the hood and on a hot day? and is this a 1.8L engine or a 2.8L engine ? if you can get he car started by puting your foot on the floor and cranking it during the times i pointed out then it is likely a dirty throtle body heat sensor which is located in the neck of the tube that connects to the throtle body. either cleaning or replacing this sensor will fix it.