Random problem with car key fob.

[Knipples]

My key fob I usually use to lock and unlock the car doors has suddenly stopped working. I usually press it twice to lock the car and once to unlock it.
Its a 52 plate car, and I am fairly certain I have had the battery in it changed once.

The reason I think its random is im not sure its the battery because the light is still coming on on the fob (just nothing happens) and because I am still able to start the car.

I would have thought it wouldnt start due to the thingy that talks to the imobiliser in the key fob no longer working if the battery was dead.

Any ideas please?