One problem related to starter solenoid has been reported for the 1996 Dodge Intrepid. The most recently reported issues are listed below.
On four separate occasions our vehicle has shifted into 2nd gear when running and could not be upshifted or downshifted. The only gears available were 2nd or reverse. The dealer replaced the solenoid twice and the tc module once. The fourth time it happened, the diagnostics did not show anything wrong and the dealer did not replace anything. The dealer stated that they were unable to replicate problem. Each time the transmission failed if the car was shut dow and allowed to cool for an hour or more it appeared to reset and operate properly for a while. If the car was driven for a longer period of time after reset the problem came back.