well I'm not an expert, but the temp has dropped lately and that's what kills batteries. You might be lucky that your engine catches first time. At the very least, get down to a battery shop and get your battery 'load tested' (even Halfrauds can do this). It would seem to me that you've got some kinda of sparky related gremlin and it's as good a place as any to start.
If your alarm still arms etc, it might be because it's got a battery backup (and THAT battery is ok?) but the car battery hasn't got enough juice to pop the motors in the doors....? Dunno exactly, but get it checked first chap.
