The plastic ring at the centre of a DVD case is designed to protect a DVD by holding it securely. A broken ring will not perform this task and can even scratch the DVD's vulnerable shiny side so that it will play erratically or not at all. Fix the ring by reattaching the plastic parts that have broken off. A few tools will be needed but no special mechanical skills, and there is no chance of damaging the DVD case.
Place a sheet of newspaper on a table to protect the surface. Open the DVD case. Upend the case so that the plastic parts that have broken off from the ring fall on the newspaper.
Place the DVD case on the newspaper with the broken ring facing up. Blow off the side of the DVD case that has the broken ring on it with a burst of compressed air. Wipe off the plastic parts that fell on the newspaper with a lint-free cloth.
Apply bonding glue to a broken part of the ring. Place the plastic piece that corresponds to the broken part back into position on the ring.
Hold the plastic piece against the bonding glue for a minute so that the glue can take hold. Release the plastic piece. Let the bonding glue set for 10 minutes. Repeat this procedure with every piece of plastic that is on the newspaper. Let the bonding glue set for a day once all of the plastic pieces have been reattached.
Place the hole on the DVD down over the ring. Press down to engage the ring so that it secures the DVD. Close the DVD case.
A magnifying glass can help you to see how to place the plastic pieces on the ring.
Wear cotton gloves to protect your hands from the bonding glue; it can stick and pull skin off if mishandled.