"no such field in civicrm_api3" after Upgrade from 4.6.4 to latest 4.7
I'm sorry for the troubles you have had (and I guess in the future you will backup before trying an upgrade). 

It's very complicated to try to determine what completed, what didn't, and how to move forward from your situation. I'd generally recommend engaging the services of CiviCRM shop that has developer experience at this point.

An approach I would recommend in this situation is to create a new CiviCRM 4.7 site, then import the data from the 4.6 database. But you there is no standard script for doing this; hence the need for a CiviCRM developer.