I can't open my iMac, help needed urgently

I have been having problems , started with email, my emails were arriving to my mailbox (gmail) but addressed to holidays in united kingdom......

1. decided to change email and set up a new one with my service provider, there was an area fault so could not use this .....(still can't use this but thats a separate issue)

2 Changed Apple id and password using my macbook.

3 Can't open my iMac at start as the password won't work.

4 spent an hour with apple support yesterday, opened mac in rescue used terminal to reset password........twice still couldn't open. so she made an appointment at local apple store in a few days time to take my mac in.

5 Thought I would be clever today and try reset password again, didn't work. Then did a complete restore from my separate backup hard drive (3.5 hrs) to try get iMac open.........no joy......

CAN ANYONE HELP ME AS I DESPERATELY NEED MY IMAC , FOR WORK. THANKS