Hey have you ever found a solution to your problem??? My 96 ES300 started doing the same thing. If I turn on the car from a cold start and shift it into drive it doesn't move and I can tell that the transmission never really switched. But if I put it into reverse I can feel it switch and I can reverse. If I leave the car in drive for about 3-8 mins the car finally goes into drive and I can drive around. But this only happens when I start the car from a cold start. I recently changed the transmission fluid and that didn't solve the problem either.