I have a 96 ram 1500 Laramie 4x4 I go to turn the ignition off and the truck stays running, replaced the lock cylinder and ignition switch. Through frustration I did find out that if I hit the steering wheel it will shut off but then some of the dash lights stay on such as abs oil light etc. Also stereo does power down with ignition. I think it might be the remote start shorting out I dont have a fob so removeing it wont bother me I just need to know if its it before trying to remove any help would be appreciated. Update realized the steering wheel isn't locking but park is

 

You apparently have a short somewhere. If you don't use the alarm, get rid of it. One less item to complicate matters.

 

I planned on removeing it but if it isn't the probable then all I accomplished was a very minute weight reduction and if it is fully functional then all I need to do is buy a programmable fob and I turn increased the value

 

Then go looking for the actual problem. You have power, when you shouldn't. Is the new ignition switch actually doing its job? Is it adjusted properly? You can download the 96 service manual from here. Wiring diagrams are in 8W. See if you can figure out where the improper power feed is coming from.