Not that this info will help with repairing an already problematic install, but I'm curious about something. On several separate occasions, all of the preinstalled modern UI apps (weather, music, store, mail, calendar, etc.) stopped working after removing the Windows.old directory. I've replicated this from a clean install, and have found other users complaining of the same issue on the technet forums.I experienced this on 10130, 10162, 10166, and 10240.
Did you by chance delete the Windows.old directory sometime just before the apps started failing?