It really is a matter of personal preference at this point, since your staining the cabinets a dark color. You could sand lightly until the poly is off. Personally here's what I would do. The cabinets are 35 years old I would give it a fresh look. Start off by removing the hard ware off the cabinets and taking off the doors don't forget to number them in the back, you won't lose track. Then begin stripping it completely which it is fairly easy to scrape off with a plastic scraper. Then sand down whatever is left which shouldn't be much. Go to your local home improvement store talk one of the associates they will help you pick out a stain. Apply the stain with a soft rag, dry with a paper towel .Once the stain is dry apply your poly. You should have beautiful cabinets looking brand new like they did 35 years ago.

Hope this was helpful best of luck ..

ThePaintAvenger

Hi Terri you can give Citristrip a try.

The Citristrip 17 oz. Safer Paint and Varnish Stripper can be used on wood, metal and masonry surfaces to remove latex- and oil-based paint, varnish, lacquer, enamel, shellac, acrylics and epoxy. The easy-to-use formula has a fresh orange scent for use indoor. Efficiently removes latex- and oil-based paint, varnish, lacquer, enamel, polyurethane, shellac, acrylics and epoxy.Removes 7 layers of latex paint and multiple layers of oil-based coatings with 1 application

• Also removes pigmented wood stains

• Can be used on wood, metal and masonry surfaces

• Low-odor aerosol formula has a fresh orange scent

• Non-corrosive

• Non-toxic formula

• Biodegradable

Good luck ,ThePaintAvenger

Withstands up to 3,050 lb. of hydrostatic pressure.If its a combination of drywall and cement then elastromeric caulking for drywall and drylock for the cement.Seal it all up with a drylock or behr waterproofer.You can find this at Any Home depot.