The FRM is a module located near the driver's left calf, so is the CAS. The FRM monitors the keyslot to see if a key has been inserted and the lock tumbler turned to lock/unlock, then it sends a message to the JBE module to send voltage to the lock actuators, which is what actually is the lock/unlock mechanism. So either
- the lock tumbler electronics is not sending a signal to the FRM
- the FRM is not receiving the signal from the tumbler
- the FRM is not sending a signal to the JBE
- the JBE is not receiving a signal from the FRM
- the JBE is not sending a signal to the lock actuator
- the lock actuator is not getting a signal from the JBE
- the lock actuator is getting a signal but is unable to actuate itself
so the diagnosis is finding which of two modules (FRM or JBE), or which of two devices (tumbler electronics or lock actuator), or if the wiring in between any two of the four components... is bad.
Since you said that the metal key does not unlock things, we don't need to bother (yet) with why the radio signal (between fob and car) works or doesn't work... we gotta get the most basic part to work first!
As for patents' comment in post #4, the mechanical key has a chip in it with an ID code; so it is possible to somehow get a key (used car, y'know) which turns in the lock but has the wrong ID code...so the signal will not be sent to unlock your door!
And someone has reported that their (non-CA) fob battery (rechargeable, gets charge while in the dash slot) had gone bad, and he had to buy a new fob from the dealer (which worked!)...trying to replace the rechargeable battery (eBay) himself failed to get his fob functional again.