Welcome back:
As far as a third gear solenoid, it is all controlled by the PCM. However, there is a line pressure switch that I really question, especially since you had fluid forced from the dipstick. The bottom line is if third gear isn't working at all, either there is a problem in the valve body or a pressure issue. I have found nothing on testing line pressure. However, I did find information on the line pressure sensor and control solenoid. Here are directions related to them. This may be a consideration before replacing the entire transmission, but that would be your call. The attached pictures correlate with these directions.
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Removal
See Picture 1
1. Remove the valve body from the transmission See: Valve Body, A/T > Removal and Replacement > Removal.
2. Remove the electrical connectors from the Pressure Control Solenoid (1) and the Line Pressure Sensor (2).
3. Remove the screws (6) holding the Pressure Control Solenoid (1) and Line Pressure Sensor (2) to the valve body.
4. Remove the pressure control solenoid and line pressure sensor from the valve body.
INSTALLATION
Picture 1
1. Install the Pressure Control Solenoid (1) and Line Pressure Sensor (2) into the valve body.
2. Install the screws (6) to hold the Pressure Control Solenoid (1) and Line Pressure Sensor (2) to the valve body.
3. Install the electrical connectors to the Pressure Control Solenoid (1) and the Line Pressure Sensor (2).
4. Install the valve body into the transmission See: Valve Body, A/T > Removal and Replacement > Installation.
Image (Click to make bigger)
Saturday, February 23rd, 2019 AT 5:15 PM