Some auto parts stores have a remote tester ( usually near the battery display ) that will check if a RF or IR signal is being generated.

Yours will have IR for the steering column lock ( can't test this at the store ), I'm not sure if it has IR or RF for unlock. Anyone know if they can unlock the car if the remote isn't pointed at the car?

If you have a video camera you can test an IR remote by shining it at the camera. Not all camera are IR sensitive so test it first with your TV remote.

The remote might need resynced. On the just prior generation single button flip key, press the button 2X then insert key in ignition and turn to run position.

I'd suspect the same procedure was used for the electronic key. This should be in the owners manual also.