Neil,
I agree with JIMnWV - but it does sound like your switch may have gone bad but if you don't have one, pick up a cheap continuity tester and check to see if you get continuity between the "bat" and other power terminals with the key switched to either of those positions (without wires). If not, you may very well have a bad switch but also check for corrosion on the terminals. This is often something people don't even consider.
The best way to address corrosion on the terminals is getting a small wire brush, preferably brass and with all wires removed and the terminal screws loose, spray a little WD-40 on them and with the brass brush, brush each terminal vigorously then wipe them down with a soft clean cloth. Reconnect and see if that helped otherwise, sometimes corrosion can occur inside on these old switches which if thats the case, you will need to replace it.