Servicing stuff is hard, its good that you've got a schematic.
Only as hard as we make it.
With no parts makings, indeed quite difficult however when devices are clearly marked....we all know how to use a search engine and find datasheets don't we ?
I too once thought SMPS as magical voodoo but study of Typical Application circuits in nearly every SMPS controller datasheet and breaking the circuit into its small and simple building blocks has one discover SMPS is not magical at all and really quite simple.
AC supply must be rectified to HV DC from which dropper resistors*
1 provide current for the controller to start then the flyback winding*
2 takes over for continued operation.
*
1 If these resistors are open or read high the SMPS may not start.
*
2 Flyback supply is rectified and fed to the VCC supply where both the diode and VCC cap must be in good order for reliable operation.
On the secondary side diode failure can be attributed to overload, probably from exceeding the stated overload cycles its datasheet specifies when the output caps fail due to high ESR and subsequent heating, drying the electrolyte and leading to internal shorts.
Low quality Low ESR caps are common resulting in short SMPS life.....