Unable to "Sign in to download from the App Store" after Erasing MacBook Air "Core 2 Duo" 1.86 13" Late 2010

I received the subject MacBook Air (Model A1369) from a relative and erased the hard drive using the Mac OS X Utilities (CMD-R) when booting up.

In attempting to "Reinstall Mac OS X" (2nd option of 4), it brings me to a page:

After I accept the EULA, the next screen I get stuck at:

When I put in my valid AppleiD (and I checked my password by logging out of another computer and then re-signed in), it does not accept my password but instead gives me the message in red below (I deleted my AppleID and password, for privacy):

My phone and computer receive a message saying that an attempt to log in to my AppleID has been made, and pops up a six-digit code for authorisation purposes, but no opportunity exists to enter the code on the MBA.

What is strange is one of the screens above asks if I want to create an Apple ID - but no such opportunity exists.

Also, I did choose "Forgot?" but it just hung the computer.

I also changed my network, where it prompted me to enter the password, and I did that, so I figure it is connected to the internet...

Any ideas?

Thanks in advance.

Ken