I didn't read all the replies so I don't know if this has been solved or not.
You can just set the iPhone into Recovery and restore from there; iTunes won't ask for any password, be them the Restrictions passcode, the general passcode and/or the Activation Lock (Apple ID) password.
Activation Lock will still be active, it'll just not be required to do the Restore by iTunes — Activation Lock sort of resides on the activation servers not so much in the phone itself.
You can also go the iCloud route and just remotely restore the phone from icloud.com/find, as long a it's not been jailbroken it should go normal.
Don't restore a backup since they reset Restrictions settings too. I once restored an old iPhone for a friend but it had all sorts of locks on it and it wouldn't complete the restore so I interrupted the restore by just unplugging the cable ruining its to give complete information to iTunes and just then I did complete the restore — this iPhone also didn't have a working power button so entering DFU wasn't an option.
Restarting the phone can be achieved under the Accessibility settings.