2002 Saturn Vue will not go above 20 - 30 MPH

You are in "limp" mode, due to some faults that have occured, all the codes seem to be pointing toward the transmission and the transmission control module, the module is going to have to be tested and scanned for further diagnosis, or you can just replace it. There is a very small chance that the computer/module needed to be reset. And you did that by unplugging the battery. Hopefully that was the case, otherwise the module will need some further testing