Security system by-pass

That is a sign that the security system has activated with the immobilizer. The system in that vehicle isn't able to be bypassed with any easy modification and any of the immobilizer bypass kits would likely cost you more than having a new key(s) made. You say you have a working key, With that an automotive locksmith could easily cut you new keys and then program them into the system using the working key as a pattern, which saves money over them needing to contact the company for a cut based off the VIN. They can also erase the old keys to prevent someone from stealing the Jeep if they were found.

Maybe for the mechanical part of the key, but the locksmith can always call the hotline and run the VIN as needed. The big thing is the immobilizer chip in the key, for that the GM one will be probably be in the wrong code section to work. However stranger things have worked. Does the key work the locks as well? If so you might be fortunate.