Actually the transmission on a 3.0L LeBarron is a three speed hydraulically controlled transmission.

The four speed tranny is the A604 or some variation of it and is electronically controlled by the Transmission Control Module or TCM.

The purpose of the " going into second gear and staying there"
failure mode is a limp in fuction. If the TCM sees a gear ratio error it stays in second gear so that no more damage is done to the hard parts of the transmission and you can still drive the vehichle to a repair center.

Your transmission should be the three speed so that does not apply, does sound like a typical overhaul to me. I've done a few.