I know nothing of alarm systems - really absolutely nothing...
Much will depend on just where the short happened on the circuit board.
A higher than normal current will have flown from battery +ve to battery -ve - some components will have been down-stream of the short and will have noticed nothing - no effect on them whatsoever - others up-stream will have experienced a much higher current than their design spec - of these several may have been damaged - some may have been mostly unaffected and one at least may have acted like a fuse - melting with the high current and cutting it off.
A separate fuse might have been a life-saver for you - either on the circuit board itself or external to it - if this was the first thing to pop then you may have got away with it.
You may have to get handy with a test meter - to see the resistance the board presents - ohms law to calculate the likely current draw - has the accident caused a low resistance path?
Other alarm system specialists my be able to give better advice. Let's hope so...
Good luck...
November 2014
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