Apart from the obvious signs of explosion or burning, the most common cause of SMPS not starting is dried out capacitors. Look for signs of bulging tops on electrolytic capacitors or the can lifting off the PCB and exposing the plastic 'bung' underneath them. If all look OK, try changing the smaller value ones near the input end of the unit, often they are related to the 'kick-start' circuit that initially provides power to start the first few cycles of output before the main supplies take over. Their values are typically small, usually < 22uF but beware of their voltage ratings which are often high. Always replace them with ones rated to 105C temperatures, it gets hot in thos PSUs!
You could also try contacting the manufacturer TDK for a service manual.
Brian.