We have to recommend starting with diagnosing the battery draining problem. If your VW Cabrio ran for a few days with a new battery you want to check and make sure the alternator is charging the battery properly. To answer your question, more then likely, the repairs made to the O2 sensor, EVAP purge solenoid and catalytic converter are not related to the battery problem.
The noise you are hearing sounds like a relay which is trying to run but because inadequate battery current is unable to hold the relay closed position (energized).
If after you check the alternator and starter circuit and find no problems you'll need to find the source of the battery drain. It is possible a circuit is staying on and draining the battery.
To test for a drain you'll need a multi meter that can measure amperage. The meter should be connected between the negative battery post and negative battery terminal after removing the negative cable off of the battery. Once this connection has been made wait 1 minute in order to allow the computer to go into sleep mode. Do not attempt to start your Volkswagen Cabrio. You will damage the multimeter.
While trying to find what is draining your VW's battery you should not see more than 25-50 millamps traveling through the multimeter. Any amps over these numbers indicates a drain on the battery. In order to isolate the drain you'll need to remove one fuse at a time watching for the drainage to stop. The fuse that reduces the drain is the draw. Consult your Cabrio's owners' manual or service manual to find what circuits are on that fuse. The relays should also be inspected.
