Q: Password not recognised and will not reset after restore

I have 27" i7 imac it was running  and time machine backing up on mavericks but the seagate hard drive was failing so I took it to a "Apple specialist" for a new hard drive along with my synology nas containing my time machine backups. After bringing home my machine and booting it would not recognise my password.

I have tried every method I can find to reset but still no joy. Could it be possible that because the system was installed with os x 10.6 before trying to restore that the mavericks backup is not compatable?