An image with many parts will no longer ungroup. I opened it to try and edit and can't separate the objects. What happened and how do I get it working again?

Try to ungroup multiple times using shift ctrl G

if this doesn't work

Are you sure it's a group ? If you used boolean operator like path/union then you didn't group but you "merged" the two shapes and you can't the individual shapes back (except with undo)

To make sure it's a group :
select your "group",
launch xml editor (edit/xml editor or shift ctrl x),
you'll see the stucture of your document

If the selected item is a "svg:g" then it's a group and you should be able to ungroup using shift ctrl g or to select items in the group using the xml editor (just click one item under the currently selected)

Maybe that is a pattern fill added to an object, or a raster image.
Press Shift+Alt+I to convert pattern to object.