Problems uploading new images using Insert Media BUT uploading via Media Library

When uploading a new image into a post using the Insert Media button, I click the button to upload the image, and it shows the following loading info which never goes anywhere and the image never uploads (even if I go back into Media Library). Here’s what it looks like:

https://www.dropbox.com/s/5xctdbv41by3plt/insert-media-problem.png?dl=0

But if I upload the exact same image via Media Library, the file uploads instantly.