Ok, there are several things that can cause the remote start not to work. if there is anything fault codes stored in the system the computer will disable the remote starting. you will need to have the system scanned for trouble codes to know for sure what the problem is. but since you dont have a check engine light on, the most common problem is the hood ajar switch. this switch goes bad, when this happens, the system thinks the hood is open and wil not allow the remote start to work.
If there is anything you dont understand, please feel free to ask me to explain