By does not move, do you mean won't start? Or will not proceed into gear as normal? Automatic or Manual? If automatic, there is a chance that the transmission valve body was damaged in the process. Not very likely, but possible. Normally, this would only cause shift hesitations. However, in extreme cases, it may prevent the car from shifting into gear at all. Also, the shift linkages may have come loose and are not pulling the selector into the appropriate gear. Depending on your engine, they may be easy or difficult to locate. They are easy to locate in the 2.0L and 1.8T, not as easy as the VR6. It's generally best to avoid transmission work yourself. It is complicated, and not worth it, in my opinion. Is it possible? Sure. Is it practical? Not so much.
every 3,000 miles
you dont change oil on a transmission
5w30
The manufacturer recommends you change the motor oil every 7500 miles, or every three months. As the vehicle gets older. It is recommended to change the oil more often.
4 liters
My 2011 volkswagen Jetta S takes just about 4 quarts of oil when i change it. When the dealership changes the oil they put in 5 quarts and it always measures too high on the dipstick. I've read that a lot of jetta's from 2000 and on take 4.2 quarts.
about 20USD for the gear oil and 8USD for a pump. you'll need a 17mm Allen wrench and jackstands.
6.3 quarts
Why does oil light come blink on 2003 Jetta 2.0 after oil change
...on the very bottom of the engine block.
6 quarts
sae5w-40 or sae5w-30