The front derailleur cable snapped on a friend's bike, she shifted it with her hand to a rideable position, and rode for a few weeks. She asked me for help replacing the cable, though when I replaced it, I realized it couldn't shift the cable onto the big ring, as the derailleur cage touches the inside of the larger chainring, instead of guiding the cable above it. [[EDIT: Touches the chainguard, as pointed out below]].
On visual inspection, it seems like the derailleur is installed too close to the chainring, and should be 1-2mm higher. The thing that seemed obvious to do, but very likely wrong, would be to unscrew the derailleur hanger at the frame, lift it 1-2mm, and reclamp it. But this is a 30 year old bike, where the derailleur surely has never been moved. I'm sure I'd be making things worse if I tried this.
Is it possible that the cage is bent somewhere else, and there's another way to adjust it? Photos attached.