The click is the relay operating. So no click suggests various possible faults.
In my case, the obvious, but unnoticed one was that I had leaned on and latched the Emergency Stop button!
Check that first.
Then, is power available to the machine? (No blown fuse in the plug? )
Make the following checks, with the power OFF and disconnected.
1 ) Relay Failure – coil or contacts not making.
Check continuity of coil
2 ) open circuit on one of the feed wires to the relay
Check continuity of each of the wires.
3 ) open circuit on one of the wires feeding the microswitch
Check continuity of each of the the wires feeding the microswitch
4 ) Failed micro switch.
Short out each microswitch, in turn, with a temporary bridge. When it works, you have found the faulty switch.
5) Open circuit on the wires feeding the low voltage power supply transformer
Check continuity of each of the wires.
6) failed low voltage power supply transformer
Check continuity of primary (Mains ) winding.
Check continuity of secondary (Low voltage ) winding
7 ) Any blown fuses?
If YES find what it feeds and check that for short circuits
Probably does not matter about the exact order in which you make the checks, as long as you are logical and consistent in your approach. Do not flit from one thing to another.
HTH
Howard