This is an odd issue on a few Windows 10 installations that we are working on.
To work around this issue, go to this path: C:\Users\<user_name>\AppData\Local\GARMIN_Corp\BaseCamp.exe_Url_BUNCH_OF_LETTERS\4.5.2.1\user.config
You can delete this file to get back up and running. Note that this will also delete some part of BaseCamp's user settings. If you feel comfortable editing the XML file, you can remove everything that references "TaskUI.Properties.Settings" to preserve the rest of your settings.
