Two problems related to transmission not engage have been reported for the 2001 BMW 330. The most recently reported issues are listed below.
Car's transmission will not engage reverse gear. Electrical detects reverse gear, reverse lights, backup sensors and mirrors functional, transmission will not reverse, acts as if car is in neutral. Noticed online it is a very common problem. Cost of repairs: over $5,000. Price paid for vehicle in perfect condition: $9,000. Mileage, 105k.
I have a BMW 2001 3330i. The car has 120,000 miles on it. I have had the car for one year, purchased used with 106,000 miles. I was backing out of my driveway when suddenly and without warning, the reverse gear disengaged. The reverse gear has not worked since, approximately two weeks. The other gears work fine. The car has an automatic transmission.