Allyb was just saying the other week(?) that he just changed his battery, think he might have been having similar problems to you, but perhaps not as bad, with the engine being slow to start, does the alarm blip every now and then when you start up the car?
Oh and is the alarm not an added extra... the immobiliser light on the dash I thought was designed in, the alarm was fitted after...? the alarm If I am right is an aftermarket one, rebadged for Subaru...? not sure about that though, but no one makes better alarms than alarm companies, why make them yourself...