How did they test the voltage regulator? If the output is low, and you've got a code then there is a likely problem with it.
These code are from the 2001 factory service manual. Why they differ from what Magnethead posted I don't know. They're close though.
P0622: An open or shorted condition detected in the generator field control circuit.
P1682: Charging system output voltage low.
Unfortunately, the regulator is built into the PCM.
Start with the basics. Make sure all connections are clean and tight. Then, post back with what you are getting at 2000 rpm. Use a digital meter at the battery, not the one in the dash. It should be between 13.6-14.2.