Power on your system. Wait for the "Grub loading" message to appear and, depending on your Linux distribution, get ready to hit either any key or the ESC key to enter the grub boot menu.
Grub loading, please wait ...
Press ESC to enter the menu
or
Grub loading, please wait ...
Press any key to enter the menu
press esc (or whatever it says these days) and you will get a menu with different configurations to boot into. Pick the one called failsafe.
This will give you a terminal.
In the terminal, you want to read the files in /var/log/messages (and /var/log has x-server logs too - check them), with any luck there is a clue in there.
You should take this opportunity to make a backup.
Also run a filesystem test:
man fsck
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