I have old 1084(s) monitors that make funny high pitched sounds and don't light up the LED.
Me too have had the same problem on my old 1084s monitor, and I had to send it to a local TV repairman (when it first appeared the problem, there wasn't any commodore service left).
The fault should be on the high voltage circuity, but it won't cost you more than 40-30$
The annoying thing now is that if I try to move the screen horizontally on the extreme left, the display vanishes with a high frequency buzz (somethin I try to avoid doing).
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Subaru Stella