I have found http://forums.macrumors.com/threads/corrupted-user-account-el-capitan.1932063/ which indicates that I am not the first to experience this issue.
enric0 advises the solution to be:
"
If I understand correctly you have another admin account that is working fine, then given the situation, I think the easiest fix is to rebuild the broken account preserving its directory structure. It may sound scary but it’s actually quite easy and fast. Before proceeding is always better to make a backup of the sensible files you may have in the broken user's account folder.
First you have to login using the working account then open the system preferences and go to "Users and Groups". From there you have to locate and select the corrupted account and click on the minus button to delete it (maybe you have to unlock changes clicking on the lock icon first).
At this point the system will prompt you with options to "Save the home folder in a disk image", "Don’t change the home folder" and "Delete the home folder". You must select "Don’t change the home folder" to leave the account's home folder as is, in its current location inside Users folder, and then you have to continue by clicking "Delete User".
This way you have deleted the user account but you have preserved all its local data and preferences.
The system may rename the home directory of the deleted user by appending "(Deleted)" to the folder name itself, in this case you have to rename the folder yourself by giving the same name it had previously, e.g if the user’s name is Joe you have to rename "Joe (Deleted)" to "Joe" without any spaces before and after.
Now you have to go back to "Users and Groups" and add a new account by clicking on the plus button, here you have to carefully give the exact same full and short name to the account as the name of the user folder (e.g. Joe) then the system will detect the existing home folder with the same name of the user account and will popup a dialog warning with the option to use that folder for the new account home, you have to click "Use Existing Folder" then, after the setup complete, the account will be restored. Now you should be able to login with the restored account and find all your files and apps working.
Maybe this is not a perfect solution but it not require you to move files from an account to another and for sure is better than modify system files by hand if you don’t have the experience and the know how to do that.
P.S. If you do not have another administrator account there are some other steps (a bit more tricky) involving reboot in Single-User mode to create it before."
I intend to test this once SuperDuper! completes the backup.
