eric:
It is unlikely that the switch is bad..... but if in doubt it is easy enough
to test..... besides, if just the switch were bad you would still be able
to turn the television on and off with the remote control. Does that make
sense to you?
Things for you to check next:
Is standby power getting to the micro?
Is the power relay clicking?
Check the electrolytics near and around the power relay..... usually a 22uf
cap is suspect.
Is the HOT good?
Check solder joints on HOT, Flyback and H Driver Xfmr.
Check for open low-ohm power resistors around power supply and near flyback.
Of course, since you did NOT post the very important model number of your
television, I am only giving you wild guesses..... I know that it is obvious
to you that NOT all "Sony Trinitron 21" televisions have the same components
and are NOT designed the same exact way.
Next time you post for a repair suggestion be certain to provide the MODEL
NUMBER if you are hoping for any specific and halfway accurate replies.