A new Designer update has been released that resolves the issue on Mark's PC.
During startup the Designer tries to delete the temporary cache folder in the user %LocalAppData%\Cefsharp\cache folder. The Designer aborted when it tried to delete the folder when it did not exist. It should have looked to see if the folder existed before it tried to delete it. Today's update puts the necessary checks in place to properly delete/create the folder.
This is the folder that the embedded chrome browser will use during your editing sessions. I want to start each Designer session with an empty cache so that projects will always load the latest JavaScript and CSS.
If this latest update does still does not resolve your issues then just like in Mark's case I need to remote into your PC to have a look.