Back in the day I repaired hundreds of CBM monitors. By far the poorest of the bunch were the 1950's and 1960' (followed by the later version of the 1084S). They will die because it's a Tuesday, because you wore a green shirt, because the moon is half full, because you pressed the amiga key too hard..... The components were cheap and when they would blow, the poor design would take out a fist full of other components. Also the flyback transformers were weak. If that goes out it would be very hard to find a replacement. Honestly I'm surprised someone still has a working one at all these years, but some do exist.
They were so touchy that yes in fact... if it didn't like the frequency of your video card, if it was a bit off from "1960 perfect", it could push those 25 year old components over the edge.
There is always hope. Cold solder is always something to look for on old equipment. The scenario you describe doesn't sound hopeful though. Replacing all the eletrolytic capacitors can often bring things back to life if more serious damage hasn't occured yet. Also make sure all dust is blown out of the case. Dust can cause shorts around the high voltage areas. If you're not experienced with monitor repair, definitely leave it to someone who is. Monitors can give you a nasty burn or even kill.
To anyone else thinking about buying an ancient monitor.... spend your money on a flicker-fixer/new video card and plug in to a new monitor instead.
Plaz