What happens when the cable is not attached to the rear derailleur? does the shifter work then?

Have you tried replacement cables (inners and outers)? Are the cable still correctly routed, has a ferrule(cable end) come out of its guide?

For replacements if needed, stock the 1993 came with Atlus A10's, these were rapidfire+ combined brake /shifter (STI), modern 7 speed shifters can be used, you would need to get an STI version, or seperate brake lever, which ever you got, wou but you would need to get non-v brake version.