Thanks everyone.
There is only one box, associated with the newer alarm (which I myself cut the wires to 4 years ago in a moment of desperation as the damn siren would not go off).
I have to think the other wires have been dead even longer. So I'll be cutting 'em off today.
I am not very knowledgeable about electrical stuff (the most I have done is change out a light fixture), so apologies if I seem a bit paranoid.
I have two non-functioning alarm systems in my house. Both have magnetic sensors on my kitchen bay window, and I decided I was tired of looking at...