Remove all broken button caps. You might want to completely break those with a partially broken stem using an sharp blade.

Clean the button caps, and the parts which will have to be glued back using isopropyl alcohol.

Find something to put under the front bezel so the buttons caps won't be pressed back up when gluing them.

Cut 5 pieces from a light cardboard box, 5mm x 15mm, and fold them in a U shape. These will help holding the button caps and keep them centered in place.

Cut a dozen pieces about 1mm x 4mm from a pill blister or some other PVC blister. These will be used to reinforce the part we glue back.