I have a 1996 ram 2500 with the V10, 4-5 times in the last week I have went to start it and all I get is one click inside, battery is good and all connections that I have check, I noticed that if I move the shifter it eventually starts, I have replaced the neutral safety switch because my back up lights aren’t working. Didn’t not help. Any ideas??

 

Make sure the shift linkage is adjusted properly.

Since you are getting a click, I am going to guess you are hearing the starter relay. It's in the PDC under the hood. You can try swapping in a different relay, (horn) and see if anything changes. If not, then see if you are getting power at the solenoid on the trigger wire. If you are, and the starter still doesn't turn the motor, replace the starter.