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Single user mode does not require a password. What happens exactly?
Reboot into the Recovery HD by choosing the ‘Apple‘ menu > Restart, then hold down the ‘Command’ + R’ keys on the keyboard during the start up process. If you can't get to that menu just hold the power button for 10 seconds until it shuts down. Then start it up again holding those keys. When you see the Apple Logo you can let go.
When the machine boots you may have to choose your language then you will see the OS X Utilities screen. Select the Disk Utility and then Continue. Then in Disk Utility select Macintosh HD in the left column (if there are two with that name or it is named something else choose the first indented item) and then on the right select the First Aid tab then select Run.