When the battery; gets low or is not hooked up, the immobilizer can get goofy and cause problems, essentially gets "confused" about which key is matched to the car. I would start troubleshooting the problem; by removing, the pos/neg cables and touching them together for thirty seconds, this will do a hard reset of the computer. See if that helps; other then that being the problem, you need to figure out what is actually wrong. The remote portion of the key and immobilizer, are two different systems; so one can work fine and the other not. A low battery; will cause immobilizer problems, I would have the whole charging system checked and make sure it is working ok. I would also; have the car scanned for trouble codes and see what they say, you most likely will have a bunch... because the battery got run down and every computer in the car, was not able to work correctly with low voltage. Save the codes and clear the codes, see if any come back... after the battery/electrical system are fully charged. Worst case scenario; you might need to have the keys "re-matched" to the speedo cluster/immobilizer; using a program like VCDS or have a dealer do this for you.
When you start the car; does it start and then seconds later die, with the immobilizer icon blinking in the speedo cluster? That, would be the classic case; of the immobilizer kicking in and stopping your car from starting. If you have another key; you can try them and see if the problem goes away or leave the key in the ignition (on) for awhile and that usually will cause the immobilizer, to reset and then start. If this is the case; it will usually throw a code "engine blocked by immobilzer".
If it isn't starting: there is no immobilizer icon blinking in the speedo cluster, then you have another problem. This most likely, not the immobilizer and you need to check other things that would explain the no start or hard start issue. I would check fuel pressure, charging system, and/or speed/crank sensor; many times a scan might show a code, to put you in the right direction of the problem.
This page: discusses immobilizer issues and walks you through, the typical issues related to it, how to start troubleshooting the problem:
VW and Audi key, remote, and immobilizer FAQ and troubleshooting
General introduction
Immobilizer FAQ and troubleshooting for VW and Audi, with key replacement tips | VW TDI forum, Audi, Porsche, and Chevy Cruze diesel forum
When you start the car; does it start and then seconds later die, with the immobilizer icon blinking in the speedo cluster? That, would be the classic case; of the immobilizer kicking in and stopping your car from starting. If you have another key; you can try them and see if the problem goes away or leave the key in the ignition (on) for awhile and that usually will cause the immobilizer, to reset and then start. If this is the case; it will usually throw a code "engine blocked by immobilzer".
If it isn't starting: there is no immobilizer icon blinking in the speedo cluster, then you have another problem. This most likely, not the immobilizer and you need to check other things that would explain the no start or hard start issue. I would check fuel pressure, charging system, and/or speed/crank sensor; many times a scan might show a code, to put you in the right direction of the problem.
This page: discusses immobilizer issues and walks you through, the typical issues related to it, how to start troubleshooting the problem:
VW and Audi key, remote, and immobilizer FAQ and troubleshooting
General introduction
Immobilizer FAQ and troubleshooting for VW and Audi, with key replacement tips | VW TDI forum, Audi, Porsche, and Chevy Cruze diesel forum