You have mentioned you don't think the SKREEM is 'there". The SKREEM is your "FOB receiver". If the SKREEM is not there, the FOB buttons wont work but the console button will.

Problem is, if the SKREEM is gone, what is the ECU getting it's start permission from? This is my basic diagram of the SKREEM/BCM/Console switch/ CLP-SSM
If you put the key in the door lock and turn it to lock and unlock, does the passenger door, trunk, etc. lock and unlock with it? If so, the SKREEM is there and maybe the SKREEM's FOB receiver function has died.