You are getting high voltage _to_ U1, not through it. It's effectively a switch, controlling the current through the transformer winding.
It also uses the high voltage while it's switch is open to produce its own low-voltage supply & cannot work without that.
As I said earlier, check for voltage on pin 2 (relative to 5/6/7/8).
I'd guess somewhere roughly around 10 - 18V. Wrong guess - see the edit below.
If there is no voltage there, the IC is dead - or something in C9 / C12 / 15 is leaky and pulling it down.
Edit - going back to the data sheet, pin 2 is at 5.85V in normal operation.
At anything lower than that, it will remain in shutdown.
Also, a higher voltage from an external source forcing current in to that pin causes the device to shut down, as an overvoltage protection system.
If you see a momentary voltage across the capacitors on the secondary when you connect power, that overvoltage trip could be the cause.
See the section in the data sheet about the "BYPASS/MULTI-FUNCTION (BP/M) Pin"
Edit 2 -
Just zoomed in on the schematic and noticed that R15 & C12 etc are marked as "NC" - if they are not on the board then the IC is in pure stand-alone operation and should only ever have 5.85V on pin 2, from its internal regulator.
If C9 has failed or drastically changed value that could prevent the IC functioning properly.