Unity hangs if the current Visual Studio installation is broken. If Visual Studio fails to open, then Unity's progress bar indicating that the IDE is being opened will never be dismissed, effectively hanging the Editor.

Repro steps:
To reproduce you will have to produce a broken version of Visual Studio. One option for achieving this could be removing components from "Control Panel->Uninstall Programs" until it can no longer open.

Another option would be to start installing a fresh Visual Studio but rolling back the process or rebooting the PC during the installation phase. A broken Visual Studio will show a message prompting the user to reinstall the product and will not start.

After successfully reaching this stage, double click on any script file in an open project. Unity will hang showing the "opening in Visual Studio" progress bar.

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Workaround: reinstall Visual Studio properly.