You can learn more about game cache verification here Verify Team Fortress 2 and other mounted games, if any Press 'Verify Integrity Of Game Cache' button.Select 'Properties' from the dropdown menu.If that doesn't work for some reason, you can do it manually: Sometimes game files might get corrupted and a file verification is necessary.
If when you start Garry's Mod the screen is black - your display settings might be wrong.