1994 Dodge Ram shut off problem

Remove the covers on the steering column and unplug the ignition switch to see if the engine stops. If it doesn't, swap the automatic shutdown (ASD) relay with a different one like it. If that works, replace the relay. If disconnecting the switch works, most likely a new switch will solve it, but there have also been a few problems with the cam cracking on the end of the key cylinder. Normally that will cause the switch to not quite reach the crank position, but I suppose it could do the opposite and not pull the switch away from the "run" position. Check that cam before replacing the switch. If it's loose or cracked, the dealer has a repair kit for that.