If the short is the feed wire to the master switch then it would indeed cause all locks not to work. If there is one or more shorts after the switch then it would effect whichever locks are being fed by those bad connections.
That click may be a remote relay for the locks but I'm unsure if there is one in the wiring or not. You need to go to each switch with the accessory on and test if there is power to them. If not then you know your problem is before each door in the wiring, at the main/driver switch, or even upstream before that.
I assume you checked your fuse? If the fuse is separate from the windows it's a possibility.