No power to burglar alarm

Sounds like a fuse may have blown as well as the battery running flat. Its common on certain panels that when the battery is run flat it blows a fuse usually the power fuse on the pcb, clearly not the battery fuse as placing a new battery on the system it powers up. I would use a cheap meter to check the continuity of the fuse after its been removed for the panel. The fuse rating will be written on the fuse, and you can get fuses on ebay easy enough. You may have a 3A fuse you can swap in the fused spur, the panel may use a lower rated fuse between the incoming mains and the transformer. Caution that the system is potentially live, replacing the fuse isn't difficult but caution should be taken if in any doubt call a local alarm professional. Using an incorrect fuse size could damage your system.

The power from the fuseboard to the alarm system will pass through a 3amp fused spur unit. The 3amp fuse has most likely blown that is why your battery is now running your system, the battery has then drained after 24hours totally killing your system. Change the fuse (3amp only) and then replace the battery. Job done!

You need to get an electrician to check if the power is getting to the incoming side of the alarm. If not it may be loose connection in fusebox or a fault along the cable. Where are you based??