I have the same problem with my 2000 neon as you did. the alarm goes off, the door locks go off by themself & the dome light fades in and out. Do you have a part number of what your dealer changed and a phone number so I could give them a call. The dealer around here has no clue what it could be.

 

Just like I told the other guy who was having these issues, remove your EVSIIwhich is your alarm, it is located under the driver side part of the dash. There are two screws on the lower part of the panel that you will need to remove and the rest are just clips! You will have to loop the ignition kill wire or else your car will not start it should be the thick yellow wire going into your box. Any more questions let me know.