Unable to reset MacBook Air password using Apple ID, with 'There was an error communicating with iCloud' as pop up

I forgot the access code to my macbook air. When given the option to reset password using Apple Id / password, my macbook isnt accepting the correct information. I went through the steps of connecting to the internet, resetting password, via apple.com. However it still isn't working on my Mac. I was receiving the error message, "unable to connect to network" now its stating "There was an error communicating with icloud. Help, Ive had this computer for 9 years and cant afford to erase / reset all the data.

[Re-Titled By Moderator]