Electrical problems after replacing the battery

I have owned this car since 2007 and kept it in great condition, but yesterday I decided to change the battery as it had only short runs and needed recharging constantly as we only use it for doctors and hospitals so not much and it an auto and we are disabled pensioners. Anyway the new battery was fitted and everything was great that day then next time it wouldn't start and on charging the battery it set off the alarm so yanked out BTN2 and all was quiet (horn and indicators off).
Where do I start fault finding? I am a retired electrical computer technician so know my way around circuits just find cars a but of a prob at 70 but needs must.