Quoted from BlackCatBone:Terry -
Were you able to get the button rings off the front of the cabinet without damaging the rings or destroying the nails that hold the rings in place? I find that it's murder to get those twist nails to come out cleanly. I recently needed some nails and wound up destroying the plate they were holding while extracting the nails. (It was a parts game, but it still didn't feel good to ruin the plate.) If you've got a technique, I'd love to hear it.
If you are talking about the white, red, yellow and blue button rings, they are held on with a threaded screw with a nut on the back side of the door. Not nails like the front rail buttons.