The chances are high that it's a 6.8volt zener.
Can you deduce anything from the associated circuit components? For instance it looks as though the three cathodes are connected together; is that point ground? Do the working ones have ~6.8v across them? Or are they perhaps across signal input lines as transient suppression?
Finally, (though should be firstly), have you tried calling the manufacturer? I've sometimes found specialist manufacturers quite helpful with technical queries.
When I power the board that appears working properly and measure the voltage with positive lead on the anode and negative lead on the cathode I get -3.8V on CR3 and CR2 but 0 V on CR1.
Contacting the manufacturer is definitely a good idea but without being a 100% positive I believe Dukane is no longer a supplier of this equipment. Most Google searches seem to result at a company called Crest. Their website shows older Dukane nurse call equipment but it doesn't look anything like the equipment I'm working on. This equipment is quite old. Still, it may be worth sending an email.