Newbie - Key fob remote not working

[hcj986s]

From the service manual:

The hand-held transmitter radio remote control function is unavailable under the following 5 circumstances:

1. Empty battery

2. Radio transmitter outside lock-in range: If the transmitter is operated more than 256 times without reaching the associated receiver (vehicle outside range or vehicle battery disconnected), the vehicle will not recognize the radio transmitter. If the number of operations is below 1,024, it is possible to re-synchronize:
Switch on ignition with key and valid transponder.
Switch off ignition.
Remove ignition key from steering lock.
Operate transmitter within 6 seconds after the key is removed.

3. Interference due to other users on same radio frequency: The key may be used to unlock the door manually, but this will not disarm the immobilizer (alarm). To disarm the alarm, insert the key in the ignition and turn.

4. Energy-saving mode: After 5 days of inactivity, the vehicle's radio receiver is switched off. The radio receiver will reactivate after the vehicle is started.

5. Fault in hand-held transmitter or vehicle: If the LED on the hand-held transmitter stays dark when the transmitter is operated, this means the battery is empty or the transmitter is faulty. If the LED on the hand-held transmitter flashes and the alarm readiness lamp on the dashboard flashes, then the transmitter and receiver are communicating. If the dashboard readiness lamp stays dark and conditions 1 to 4 above are ruled out, then there is a system fault with the vehicle.

I tried all these and no joy. One key works perfectly, the other's LED blinks when the buttons are pressed but does not cause the readiness lamp to light up. Any ideas before I take it to the dealer?