Elecric start problem- kick start good

You have a low battery. Either the batt is going bad, or the charging system. If you stop by most auto parts stores will test both for you for free. You should charge up the battery good before driving it. If you charge batt for 3-4 hours and it does same, odds are batt is bad. Small chance it's the starter too.

Check the terminals are clean and tight on the new battery
depending on where the ticking sound is coming from it could be the solenoid or the starter motor.
use a multi meter to check if power is getting to the starter motor when the buttons depressed.
If it gets power, could mean the starter needs brushes, if it doesnt get power more likely the solenoid is bad

I would think your starter is over heating (grounding) which is draining power from batt which is making alternator use its charging capabilities to the max . starter motor is what id check. this isnt a little 14 gage wire robbing all that power so quick, it is a direct connection within the batt,starting or charging system.

clean all connections very good ( batt post connectors,gound wire from batt to frame/motor, also clean starter connections,and alternator connections) I know pep boys checked but you cannot properly check a battery unless it has a full charge!!!!! If it wont accept a full charge then batt is bad, If it charges to a full charge and fails a draw test the batt is bad. also when a draw test is done you can have the charging system checked also to make sure batt is recieving the proper charge input. all inexpensive checks, get it running and take it to a garage, 3 min test usually not even a charge most of the time. NOT A DEALER, and have them show you what they are doing. if you are a female have a male friend go with you or have it done. I dont care what anybody says!!!!!! When it comes to a inexperienced female, the DEALERSHIP,the REPAIR GARAGES will all try to get some kind of MONEY out of you before you leave their place of business.

If you are saying the starter just spins and doesnt start the engine then your starter bendits has gone bad and is not kicking out to meet the fly wheel. You while have to remove the starter and have it repaired or replaced.

- did you ever push the starter button while the engine was running?
if yes, the gear on the starter motor is damaged and needs to be replaced...

Does it keep running till the batt is flat? It could be the aircon condenser fan running - on the left as you stand in front of the car. This is a common prob with A3s of this age.
I have a '05 3.2L Quattro V6 and suffered the same prob. The batt is in the boot of the V6 and is sealed like Fort Knox so impossible to disconnect. After about 3 days with this the fan running constantly and having to put a charger on it every night I let the batt run completely flat to try and reset the complete system - no DIS lights - no starter motor clicks - DEAD. Then I jump started it and the prob disappeared completely. Everything is working perfectly ncluding the aircon. That was 4 days ago and 'touch wood' I've had no probs since. I know this won't work for everyone but it's worth a try before forking out £300+ for a new condenser fan unit. Good luck!

2001 accent Starter meshes and misses most times , good batt,changed to brand new starter also new flywheel with good ring gear etc still got same probs?

The oil light should come on when you turn the key on, then go out when the engine starts. It is NOT an oil level light, it shows PRESSURE.

Your "click" is a bad/corroded connection on the starter terminals , battery terminals, low battery, bad wires, or a defective solenoid. Charge the battery. Disconnect the negative battery cable, then the positive. Remove the nuts holding the wires to the starter, clean all connections at the starter, frame and battery with a wire brush. Get them CLEAN!! Make sure the big cables are in good shape. If that doesn't fix it, you will need a solenoid. Maybe a starter and/or relay too.

Hi,this is a low battery ,, even if you charged it may be getting bad and is not holding charge ,also be sure to clean the battery cable tarminals ,this can reduce voltage , good luck......