Derailleur out of alignment after cable snapped 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.
The derailleur cage is not interfering with the larger chainring, it's hitting the chainguard.

As you say, its unlikely the derailleur slipped down the seat tube a few mm. Seat tube clamp mounts hold on quite tightly, and if they do move you typically are able to see a line on the frame where dirt accumulated next to the clamp. The parallelogram links are pretty robust and don't typically get twisted or bent. The cage itself may get tweaked but you'd see scratches if there had been an impact.

The derailleur might just have rotated around the frame very slightly causing one end of the cage to contact the guard. You'll be able to see if this is the case because the cage will not be parallel to the chainrings.

If the derailleur has not moved I suspect that the cage is actually able to move far enough outboard to shift the chain to the big ring before it hits the chainguard. If it will not shift the chain, moving the derailleur up a millimeter or two so it just clears the guard will probably be just fine.

It's probably worth running through a full front derailleur setup process to make sure you have the limits set correctly. Park Tool has a great web page and video that walks you through the whole process step by step.

https://www.parktool.com/blog/repair-help/front-derailleur-adjustment