[Paul Clifton]

Changing the batteries won't make any difference as these are only for the remote central lock and alarm. The transponder is a chip in the actual key part which is read when you put the key in the ignition by an antennea (aerial) ring arround the barrel this in turn is read by the immobiliser which tells the engine ECU to start or not as the case may be.
If the fault exists with both keys the next cheapest thing to try will be the antenna ring.

Paul.