Get rid of the remote start all together. Not saying this is gonna solve your problem but there has been several problems in consumer service reports cause by remote start kits. Ive heard more bad than good come out of them.
To diagnose your problem i would assume its a loose wire that may have been hacked from your previous owner making more useless tweaks to the car. download the service and repair manual which has very useful wiring schematics to help diagnose and pinpoint those nightmare electrical problems...
Hope it gets figured out i feel your frustration!!