Well, I did at least find a bug which prevented the appropriate error message from being displayed.
The problem is that GD is not installed on the server. You’ll have to contact your new host.
This problem is not isolated to Connections either due to this. As an example, go to your Media Library, click any image and then click the Edit button beneath the image. You’ll notice you’ll just be presented with a broken image icon. That is because WordPress can not edit the image because GD is not installed.
After GD is installed the issues will resolve themselves.
Hope that helps!