Only a guess but it could be the transformer inside the panel that is humming . If you don't use it then , yes , shut it down.
A couple of ways are :- ( In this order)
1) If there is an unswitched spur unit next to the panel , in the main supply, lever out the fuse carrier & remove the fuse .
2) Then remove the front from the panel , there should be no dangerous voltage in there at this point...... pull the leads off the battery terminals, that should do it. Replace cover. Make tea.
3) If there is NOT a fuse unit next to the panel , isolate the supply at the fuseboard , if in doubt switch the main switch off.......remove front of alarm panel as before..........look for a 3 way terminal block with a mains type cable in it ...... there is a fuse carrier in this ...remove it & remove battery leads as before.
Posterior covering section ........please read:-
Do not mess with any wires etc until you have proved it is safe to do so .