Had a similiar thing with mine. First check the batteries are in the right way (not taking the p*ss, I did it wrong!!) and then clean the contacts. I think it has a spring contact, just bend that a little to make the contact stronger. Check the LED and other connections, its not unusual for hard wires to break, just soldered mine for exactly the same symptoms as you are having.
Other than that it could be that the alarm needs re-memorising for the signal. Bit of a coincidence though! Its telling that the alarm was switched off (in the glovebox?), perhaps they were having problems too before the current problem???
My alarm was disarmed on purchase and this was because the ultrasonics are dodgy, setting it off, I just turn 'em off these days with the ignition.