The car starting in 3rd gear is limp home mode! One of the verification methods of proper installation of the PNP is verifying that the back up lights turn on when in reverse.

Over heating ATF disables 4th gear, not 1-3. Check to see if the shift arrow is burned out - turn the key to pos II and check the lights.

You can also use a regular scan tool and plug it into the port under the coin tray if the wires are broken at the A & B diagnostic boxes. I found that sometimes if the door is left open while checking codes at the boxes, I get strange results. Never check for codes while the engine is running.

You could also verify that the OBDI boxes work by probing A-2. You might get a code there also if the car is in limp mode.

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Keeping it running is better than buying new