2001 jetta-overdrive issues?
 

2001 jetta. 100k miles. bought used. Won't shift into overdrive. At 60 mph cranking 4500-5000 rpms. Pervious owner had a "trick" written down in owner's manual: Turn ignition one click, stomp on brake 4-5 times, put tranny in between N and D and start with other hand. Worked for protracted periods, but now isn't doing the trick. Spoke with trusted, long term mechanic, suggests that the problem could be grave ($4k). Was hoping it would be a fuse, relay, etc. Any ideas? Taking vehicle in for maintenance, but wanted feedback on others who may have had similar experience. thank you.