The "click" you (should) hear is when you initially apply track voltage - not from the watchdog signal. In other words, you should hear it even if applying track voltage from a conventional transformer (no TIU).
It's true if that 5V 3-terminal regulator went south, you would not hear the "click". But the likelihood of that part failing is small. In all likelihood another cause of no "click". I suppose if you have it all opened up and can access the part I guess it's worth the 1 minute it would take to confirm you have rectified DC track voltage on the left terminal (over 20V if you have command voltage on the track), and 5V DC on the right terminal - both DC voltages measured relative to the center terminal or metal tab (which is NOT the same as the frame). You can slide the connector housing to expose the 3 terminals for measurement while still maintaining connector contact.
The 5V board set is difficult to troubleshoot. Verify the AC track voltage is reaching the board on the 7-pin connector on the smaller power-supply board; you should be able to measure track voltage between red and black wires (2 each). Then look for anything obvious...leaking, bulging, deformed, charred components. Aside from that, not sure it's worth going any further.