From research I was doing last night, I found that the transmission slippage could be due to the pressure solenoid in the transmission. It normally pulses or lowers the transmission pressure when you shift the transmission from park to reverse or drive. This keeps the bands or clutches from gripping too fast and making a clunk as it changes gears. If the solenoid is bad, it could be not putting enough pressure to the drive clutch, which would cause my reverse and 3rd slippage. Of course if it has been slipping like this for a while, I’m sure the clutch is gone. The tranny fluid is also very dirty, which is probably clutch particles. I know that worn out transmission fluid could cause low pressure, but I doubt I am that lucky.
The next step for me at this point should be to start the car and run it until it starts slipping again and checking the transmission control unit (TCU) for any error codes. This will give me an idea if the solenoid has a problem. I also should try changing the fluid and filter and measure the resistance of all of the solenoids to see if there is a bad one. I also hope that the pump is not worn out, which would also cause a low pressure condition.