My 1983 house has the original pull-out shower faucet which has been leaking from behind the faucet. Today when I pulled it out to turn the shower on, nothing happened. They don't make that same model today but is it possible to find something that will work to fix it so I can use my shower?

Shut you supply lines off and try to disassemble the valve. It may be a cartridge of a washer valve stem. Tell us or show us a picture of what you see. Most valves made in the 80s still have repair parts available even if the valve is out of production. You may have to go to a plumbers supply house and not Lowe's for the parts.