With power supplies since service information is usually unavailable you have to do a little bit of reverse engineering, or at least figure out the topology and operational blocks, and begin troubleshooting by determining the faulty block.
Any type of computer/server power supply will have a small mostly independent "standby" supply, so the very first thing to check is that it is operating properly. The standby supply needs to be functioning in order for the main supply circuit to become active.
If the standby supply is working, next thing to check, is the PFC regulator operating? Easy to tell by measuring voltage on the bulk input capacitors with the power supply enabled. Should be in the range of approx 380-420V typically, if it is only measuring rectified mains voltage then it's not operating.
If standby and PFC is ok, time to turn your attention to the main part of the power supply. Referring to the datasheet, make sure the PWM controller IC has proper Vdd voltage (refer to datasheet for UVLO turn on voltage) and that it is not "hiccuping". Ensure it's not being sent a disable signal either, if the disable pin is active it could be due to a protection being triggered (over-voltage, under-voltage, over-current, etc), usually computer power supplies have a dedicated IC handling all the protections.
Generally speaking if fuse is intact and there is no obvious damage (burnt/blown components), failures are usually due to bad capacitors, so it's worth quickly going over them in-circuit with an ESR meter.
It may seem daunting at first but once you've figured out all the building blocks and important voltages/signals in the power supply, they are all very similarly designed so generally repairing them in the absence of diagrams and schematics is not a problem.
An isolated high voltage differential probe for an oscilloscope is invaluable in troubleshooting SMPS. Can get by with isolation transformer and a regular probe too but extra caution must be observed in the primary side of supply.