How do you know? Did you physically pull out the transformer and look for shorted turns with a ring tester?
Did you put a narrow pulse through the transformer and checked for winding-to-winding bleedovers/shorts?
I'm assuming the flyback? if so, you could pulse it and measure the outputs of both the primary HV and the secondary voltage for focus/screen. Ive seen these fail in AOCs causing loud SNAPs at turn-on, monitor eventually fails with a shorted HOT. (horizontal output transistor).
You could run to your neighborhood hardware store, or harbor freight and buy a cheapo DMM for $5 to $10 dollars. Then test the output transistor on the flyback for shorts, and test the transistor on the SMPS supply. the HOT will always read a short/low ohms between B to E, because there is a pulse driver transformer to deliver maximum current to the transistor. but you should NOT have shorts from C to anything.
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