One problem related to transmission not go into gear has been reported for the 1996 Mitsubishi Galant. The most recently reported issues are listed below.
Transmission had trouble shifting for a few days. At certain speeds the transmission would all of a sudden act like it was in neutral and then pop back into gear. One day, while attempting to take off from a stop light, the transmission would not go into gear. After replacing that one, we are starting to experience the same type of problems. Especially early in the morning when you first attempt to take off the car will not move. Even after letting it warm up for 10-15 minutes the same thing happens. Sometimes it will do the same thing when you take off from a stop sign into traffic. We just pray that when we get into the middle of the road it will pop back into gear. I hate this car and I am having trouble getting rid of it. Evidentally everyone is aware of the transmission problem--except Mitsubishi.