Exact problem I had... the key has a small pcb board inside and there is a tiny 5mm button which has likely came away from the board. I can fix this for you if you are prepared to send your key to me. Failing that a new key at main dealer would set you back around 140 pounds. Reason being they dont just give you a new key, it has to be programmed to the car also.
When you press the key does the light show and do you feel the "click" if you do then maybe its not the button, but id be surprised if its not.