icloud sign in stuck in loop

I am not able to sign in at icloud.com. This is an OLD apple ID.

Every time I enter my information I am confronted with a pop up:

"You must update your Apple ID to use iCloud."

I select "Continue"

I am then presented with another pop up:

"Verify Email Address" (some more dialogue) and a box pre-populated with my ".mac" email address. I am unable to access this email, attempting to gain access through iCloud.com .

I entered a different address, one I have access to, select "Continue".

Next screen is to enter a verification code. I retrieve this from my email and enter the code, select "Verify".

Some thinking (spinning) appears to occur and I am returned to the original screen.

HOW DO I BREAK THIS LOOP???