Mark
If you lock you car with the clicker then the alarm is set. If you then manually open with the key you fail to disarm the alarm (done via the clicker), hence why it went off.
Open your key carefully over a big table (bits may fall out). As you look at the circuit board there should be two small horizontal red bars, with a weld at each end. One works the boot and the other the doors/alarm. The welds are weak and fail meaning the red bar (which is depressed when you press the key) falls off and hence nothing happens when you press the key button. This will be immediately obvious if it has happened to you as the red bar will be loose. If all in place chances are it is the battery.
The short term solution is to use your other key.
The proper fix is to find someone with a very small soldering iron to resolder the red bar at each end. My guy, a professional repairer, advised the original solder material was weak and he resoldered all four lugs in both my keys.
Good luck. If you are stuck I can PM my guy's details and you can negotiate with him re repair cost and posting the key to him etc. Loz also has a name of someone who does this.
Cheers