I also faced this problem in one of my desktop machines, but the problem came after updating the system. I haven't deleted anything. Just give a try to this, if it works or not.
I logged in my admin account using TTY terminal (CTL + ALT + F1). Before doing anything, I first ran this command-
Since it was doing disk checking in each restart. After that I rebooted my system. Then I again try to login into my account and it was successful.
There was one more problem I faced related to login process on other machine, which was not allowing me to enter password. That time, I logged in to TTY terminal and reinstalled the Gnome Display manager.
sudo apt-get --purge remove gdm
Reboot the machine or run directly
sudo apt-get install gdm
I don't know if it is a good solution.
sudo service gdm start