If all is ok we might have a deconfiguration in the system of recognition of the key and immobilizer.
Let me explain how your immobilizer system works.
The electronic immobilizer protects your vehicle by means of an electronic code integrated in the key. This is composed of an invariable personal code and a second code that the immobilizer modifies each time the engine is started.
When starting the vehicle, the immobilizer checks the personal code and the variable. If both codes are correct, the immobilizer sends a new coded signal to the engine control to unlock the engine. Without this signal, the engine can not be started, even by a bypass.
If you have a problem in the immobilizer, your vehicle will not turn on, this happens a lot when we perform works in the vehicle, it may have unintentionally done something to the battery or fuses, even a short can made the vehicle think that you were trying to turned on without its respective key and it activate the immobilizer.
In your case, the immobilizer can not verify the codes, this may be due to different factors, such as the key has been deprogrammed with the immobilizer, or that the key has no access to the vehicle, therefore the immobilizer inhibits the ignition , this type of problems is quite common so you do not necessarily have to go to the dealership to solve it, although it would be the most prudent and correct thing to do, There are auto locksmith and independent garages that can help you with your case, reprogramming the key fob, key and the immobilizer, and verify if any of the modules present damages or if there is a short.
This is done with a diagnostic tool Vagcom or with a diagnostic tool with Vw software.