If it goes to the login screen then you can rule out grub and the boot
process. It make take a re-installation of the desktop (not distribution).
You could remove ubuntu-desktop and re-install it without affecting Ubuntu
itself (you will need to get to a command prompt to accomplish that). You
could try changing the session before you login and see if that helps. It
is likely the window manager not playing nicely with your graphics driver.
Different desktops have different window managers. I always install more
than one to help troubleshoot such issues.