It sounds like you're on the right track by checking the voltage at pins 16 and 4. Generally, you should see around 12 volts or so when the vehicle is in the "On" position. Sounds like you're fine as far as the power goes.
A few things you might want to check:
OBDII Reader Compatibility: Make sure that your OBDII reader is compatible with your vehicle. Some readers may not work with certain makes or models.
Connection Issues: Double-check the connections to the new OBDII port and make sure everything is seated properly. Loose or corroded connections could cause linking errors.
Ground Connection: Ensure that your OBDII reader is able to establish a good ground. You might want to check pin 5 (ground) to ensure that it’s properly connected.
Try Another Reader: If possible, try a different OBDII reader to see if the problem persists. This will help determine whether the issue is with the reader or the vehicle's OBDII system.
Vehicle Issues: There may be underlying issues in the vehicle’s ECU that are causing the reader to fail to link as well.