Installing Simcity w/ Origin defunct

Can I please get a step-by-step on how my problem with installing Simcity (2013) can be fixed?

• I own Simcity (2013) on DVD.
• I am installing Simcity on a new Windows 10 machine
• Simcity (retail dvd install) requires Origin before copying game files
• My EA login does not work for the Origin installer
• Thus, I cannot install Simcity at all.
  
  Note, I have not previously played Simcity throughout the entire duration of EA Launcher, and if I have an origin account, I am no longer readily in possession of it.  However, I do have a modern EA account, A Simcity DVD and an authentic CD KEY.  It seems sensible that with these three things I should be able to play a game I have purchased and possess physically.  
  
  Please advise on how I might install Simcity so I can get Update 10 for offline play.