Fixing Power Adapter

I have an old AC power adapter that outputs 5V and 12V at 1A each with combined total output of 15W.  It stopped working.  I opened up and found the 2.5A input fuse was blown.   The primary side was shorted.   This offline power switcher seemed really simple.  There did not appear to have a controller IC; it was made entirely with discrete parts.  It did not take long to locate the faulty component, the primary side MOSFET switch, 2SK1535, a 900V 3A power MOSFET with 4-Ohm Rdson; all three pins were shorted.  It is a flyback switcher with two secondary outputs and an optocoupler off the 5V.





The first question is how it generates PWM signals.  Besides the main FET switch, the primary side has only one additional transistor. But the primary side has one auxiliary coil, which provides the positive feedback for oscillation.  The secondary side does not seem to even have a voltage reference, so how does it regulate?  There are only a transistor and a POT that feed the optocoupler.

After replacing the faulty MOSFET and the blown fuse, the switcher works again.  But one problem with the circuit is the lack of short-circuit protection.  The primary side switch can turn on hard and destroy itself before even the fuse blown.