There are numerous ways to solve this. Noted that you tried to chown .Xauthority with the -R switch and probably you tried it with a sudo, but again - try this version;
$ sudo chown pi:pi .Xauthority
$ sudo apt-get update & sudo apt-get upgrade
$ sudo reboot
In case that doesn't work, since you have access to the CLI space at [ALT]+[F1], you can always as a resort try to save necessary files by starting desktop with superuser with
$ sudo startx
Also have a look at for any quirkiness
$ sudo nano /etc/rc.local
at the bottom just above "exit 0" and have a consideration with commenting out a potential line familiar from a recent install with a #
Reinstalling the OS as a solution is seldom necessary, anything can be fixed but in case there isn't any crucial work lost in the process it can be a good time saving option on some occasions.