Apple ID won't open my Mac

Forgot Your Account Password

For Lion, Mountain Lion, or Mavericks

Boot to the Recovery HD:

Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.

When the menubar appears select Terminal from the Utilities menu.

Enter resetpassword at the prompt and press RETURN. Follow

instructions in the dialog window that will appear.

Or see:

Reset a Mac OS X 10.7 Lion Password

OS X Mountain Lion- Reset a login password,

OS X Mavericks- Solve password problems,

OS X Lion- Apple ID can be used to reset your user account password.