Not sure what you mean by keyless module... But if you are refering to CAS than that is a whole new subject to begin with.
I have the same problem with my remote and I have tried eveything. I even started a new topic about it.
Assuming that you have tried everything just like me (battery, key initiation, CAS reset...etc), try this and tell me if it works. I hope it does for my sake as I couldn't try it because I am out of country:
Note 3: procedure to manually update the remote control for E60, E61, E63, and E64 (pre-9/05 vehicles):
Sit in the vehicle, close the driver's door, fasten the safety belt and do not press the brake pedal.
Insert the remote key and turn the ignition to position 1 (KL-R).
Press and hold the central lock button located between the center vents.
Switch the ignition to position 2 (KL-15) while continuing to hold the central lock button.
Continue holding the unlock button for approximately 10 seconds after pressing the start/stop button. The gong will sound to indicate that the transfer process is complete.
Remove the key from the ignition.
Repeat the procedure for any additional remote keys.
Note: The brake pedal must not be pressed while performing this procedure or the vehicle will start and this Manual Remote Control Update procedure will be cancelled.
Good luck.