I have been having almost the same problem for several months. None of my metro apps, including windows store and PC settings, would open. The only exceptions were apps that open in desktop view, and the desktop app itself.
I found that that other profiles on the computer worked fine. BTW I have win8.1
Simple Fix
1. Backup all files to an external hard drive, flash drive, etc.
2. delete broken account
3. Create another account on your computer, you can do this by switching to another account and going to PC settings - Accounts - other accounts - Add account
4. create account with same Microsoft account used for the original, broken, account
5. open it up every thing should be fixed, and settings saved.
6. reload files from external hard drive, flash drive, etc.
Your Done!
Note: I am pretty Shure this doesn't work if you don't have a profile that's not broken, because there is no way,(to my knowledge) to create a new account or delete an existing account. This is because these options are only in PC settings
which is inaccessible on a broken account.