lightdm is already started . You don't need to start something manually. The problem probably is with graphics driver , Nvidia additional drivers.
Now that you have purged completely nvidia , you can try to install another version if you want.
You have 2 options.
One is nvidia-experimental-304 and the other is nvidia-experimental-310
Reboot to see if you can login without problems.
sudo apt-get install nvidia-experimental-304 nvidia-settings-experimental-304
The other "problem" with plymouth(during OS start, that with the dots ...etc) , I cannot handle it . Sometimes work good , sometimes not.
If the experimental-304 not working for you , try the 310, but first remove manually the 304.
and then try 310
sudo apt-get remove --purge nvidia-experimental-*
sudo rm /etc/X11/xorg.conf
and reboot again.
sudo apt-get install nvidia-experimental-310 nvidia-settings-experimental-310
Thanks (hope you solve it soon)