Several things can cause this if the MPU board is running.
#1 -- that stupid edge connector between MPU and driver board. Gottlieb - connectors, connectors, connectors.
#2 -- the U45 driving the relays.
#3 -- The corresponding 74175 on the driver board can be bad
#4 -- Infamous spider IC / drivers. But you ruled this one out.
With Gottlieb's - first check transistor. Can verify if it is turning on or off by monitoring the base pin of the transistor to see if the 74175 is trying to turn it on/off.
Second - reseat the MPU/driver interconnect cable to see if problem goes away or changes. If it does, repin the cable.
Does the MPU board do -anything- when turned on ... i.e. displays or lamps? Probably a good idea to make sure the MPU board really is running (can be bad power to MPU).
Ed