Hello again Michael!
A really simple test, before you even take the guts out or unscrew the case. Of course this works after the guts are removed and you have cleaned the PCB as much as possible.
1 select resistance on your ohmeter
2 place a probe on the -ve battery contact and the other
probe on the +ve battery contact
3 cycle the on off switch and observe the needle deflect from
high resistance to low resistance.
The deflection indicates that the slide contact is working. Also, use extreme caution when cleaning the keyboard silk screening. Do not rub clean or rub dry the surface of the silkscreened numbers. They are extremely sensitive and the clear laqueur that protects them has probably degraded.
The woodstocks are very problematic. Typically when the batteries started to build up internal resistance and decay they still held a charge. This led the user to plug the calculator into the mains with the adapter while leaving bad batteries in the calculator. This has disasterous effects on the PCB and is unrepairable.
Some times you see someone on ebay state that "it worked when the plugged it in but it doesn't work now" so it must need new batteries. Well, it's too late by then!
Good luck, I have a 21 here that looks mint outside and gave an erratic display. The batteries were welded inside from corrosion and the removeable PCB was pure blue. I soaked this in vinegar, (what else, it was a write off) and got it to work a little bit better, but still erratic.
Also, when you jury rig a power source use two rechargeable batteries at 1.2 volts each. These woodstocks become tempermental with age and two 1.55 volt alkalines may be enought to send the calc into cardiac arrest.
Cheers, Geoff