My daughter's 2010 Jetta SE had a stuck key. It would go into the ignition but not turn to the start position. I ordered a replacement lock housing (it came with the ignition switch attached). I removed the old ignition lock cylinder and installed it on the new lock housing. The key now turns fine but the car starts for about 1 second then stops (the No Key indicator lights). I thought if the ignition chip was in the key and ignition lock cylinder (the original one that has worked on the car since new) that using the same key and ignition lock cylinder would not cause a problem. Do I have to also use the original ignition switch? Or what am I missing?