Can't access Media Library in page/post editor

My client reported an issue where attempting to add images from the Media Library to pages, posts, or sliders results in a constantly "loading" page (spinning grey ball) with no images in the Media Library ever appearing. They can upload files to the library itself, but can't connect with those images in a page or post. We've been managing their site for a couple of years now and they've never had an issue like this before.