I stopped today on the way home to pick up a free Honda and there were two snippers getting thrown out and one is the same Stihl FS80 with the same problem ,the snipper runs when I put fuel down the carby but all the diaphragms have gone solid in the carby. The Stihl has 125 PSI compression so it's still good.
I feel like I remember seeing these FS80 trimmers in the eighties ,I might have a spare engine for a carby.