sounds like neutral safety switch is out of adjustment or has gone bad

 

i have 4 chevys 74 vega nomad wagon a 98 chevy venture mini van a 94 pos camaro and a 02 blazer but i also have an 05 dodge neon as well close to the stratus and i love my neon and my blazer lol i think its probably the the shifter there is a cable that goes under the column that has to lock in place in order for the key to go straight or come out and some times it can bend and not go in place try taking the plastic off the bottum of the column and make sure the cable is in.

my neon is a good car but a wiring freaking mess lol once you get all the wires in order you should be good to go on that stratus