Reboot your PC
Hold the shift key, in order to reveal the Grub boot menu
In Grub, select the recovery option (generally the second one)
In a few moments, recovery will ask you what to do. Select a root shell.
when you are the console prompt, type the following command
Inside the nano editor, use the keyboard arrow keys to navigate and locate this line. Edit it to make it look like this. Remove any instance of the word "quiet" and "splash" from this or other line in this file.
mount -o rw,remount /
Press Ctrl+X, Y and <Enter> when you're done editing, to save the file and exit.
Now update grub with this command:
And reboot your system
You *should* have no purple screen, as we have disabled plymouth. That means we will be able to see text messages that will let us know what is going on with your setup.
This system *will not* boot up to a desktop yet, unfortunately. You'll be again at a console prompt.
If the system is not asking for your user/password, switch to another VT using Ctrl+Alt+F1 to F6
See if the command above does get you to lightdm and to a graphical session.
sudo service lightdm start
Use Ctrl+Alt+F1 to F6 to get back to the VT you were using in case all you see is a text screen after the command above.
I'll soon ask you what Video Card you have. If you don't know the answer to that, take the opportunity to run this command:
If you are not presented with the option of using your user/password to login at the console, take note of the last text messages you see on your screen and please report them back here, so we can continue.
lspci | grep -i vga