car beeps when driver's door open but key removed from ignition

Car beeps when driver's door open but key is removed from ignition like the
key is still in ignition but not when any other door is open. Beeping used to
stop when key re-inserted and wiggled then removed or tapping the steering
column.   Now Key fob won't work to lock/unlock car.  Dealer tech says it's
due to aftermarket remote start that previous owner installed.  I believe it's a
loose wire in the ignition or steering column, but the dealership doesn't seem
to believe a woman.  Frustrated.