Does anyone have any advice on what type of glue to use?  All 4 clips need regluing.  I also have to figure out how to remove the clips from the sliders.

Thanks in advance for any advice!

I use epoxy with good results. In the UK it's called Araldite Rapid.

Hi! A flat screwdriver would do a good job to remove them. But why? For regluing them you must know the exact position and this is in the cabinet itself. Otherwise, they will crack soon again.

I would not recommend glueing them back on the main unit. There is a danger that you will get the glue in places that you don't want it!

I lever the clips out with a screwdriver one pair at a time and it has always been obvious exactly where they go. Don't remove the old glue as you will also remove the black paint from the glass. Simply stick them back with the minimum amount of epoxy, put the glue on the metal bracket only and it won't show.

Oh yes, of course, if the old glue is still on the glass, it can be a perfect frame! But does this happen often? 

Every time so far!

Excellent advice; thanks!  'Found 2 online sources for Araldite.  The old glue is indeed on the glass.