Thank you for using just answer.
Clarify this please-
you stated alarm and starting at the same time?Are you saying that the alarm is going off and while it is going off that the starter is engaging itself?
Yeah that is definately an aftermarket system.
Remote keyless entry is only wired to lock control wires, if the starter runs when the alarm goes off then this system has a remote start also.
You are going to be dealing with a control module issue on this truck, the unit will need to be replaced. You whould seek an aftermarket audio specialty shop in your area for this one.