When you measured the transformer outputs, did you have one lead on each wire from the transformer?
The negative 24 volts will connect to every relay in the panel.
Need to follow the negative side and check every splice or connection for any loose ones.
Only takes a loose connection under a wire nut to kill the entire system
Not sure why they go to a rectifier on the other leg of the 24 volts, but the 24v should come off the rectifier and connect to every switch
for the relays.
Positive goes out to the switches, then ON or OFF will activate the coils on the relay and make or break contact as needed for the lights.
The negative 24v is constantly applied to each relay.
So, find the first location from the rectifier that the 24v goes to, and use one lead at that point.
Then one lead at the first point where the negative 24v connects to the relays.
If you can take a picture of the transformer, rectifier etc, it may prove useful.
Pictures can easily be uploaded to tinypic.com and then post the link here or use the paper clip icon on the chat tool bar to post it here directly.
Post the findings on the voltage test.