I wouldn't replace anything until a better job of diagnosis can be done. It looks like you are on the right track with the VAG-COM package. It is needed to get to all the functions that are available through the data link connector. However, if you have a standard OBDII scan tool available you can read the generic OBD codes and that would be a start.
You don't mention the history of the car. Did this happen out of the blue, or has other work been done on the car? If the battery was disconnected for a length of time then the throttle control module needs to be "aligned," as VW calls it. This process causes the module to relearn its basic settings needed to make the engine idle properly. You can do this without a scan tool by switching the key to "run" without starting the engine and leaving it there for 30 seconds before switching off. During the 30 seconds you should hear the faint sound of the motor in the throttle control module running.
For the scan tool, here is what I think the people on Ebay are trying to sell you:
Ross-Tech: VCDS: Product Information
Maybe someone else here on the forum has experience with vag-com purchased off ebay. I'd be very wary that you won't get something that works properly or is supported by Ross-Tech. Personally, I have the registered version of VCDS-Lite:
Ross-Tech: VCDS: Function Table
The software costs $99 and you can buy a generic OBDII-USB cable on ebay:
USB to OBDII KKL 409 1 OBD2 VAG com Car Scan Cable Tool Auto Scanner Vehicle OBD | eBay
It comes with the shareware version of the software which you can then register to get to the enhanced features. Be aware that one of the limitations of VCDS-Lite is that you can only ever install it on one PC, although Ross-Tech will give you a one-time only chance to move it to a different PC. With the full VCDS software and enhanced cable, the software security is built into the cable, so you can use it on whatever PC you want. The software will only run if the cable is attached.
