I would like to use the Region Wall on a copy of SimCity I got from a coupon. However, I have no button in the top left corner, and pressing Enter does nothing. What's going on here?
EA is protective of their products and missing functionality on a patched game is unusual. It's possible you may not have an authentic copy.
EA delivers games using their Origin client, regardless of how you purchased your copy. If your copy is authentic you should be able to find it listed in your 'My Games' section of the Origin distribution client since EA would register your copy there. The Origin client is a free download: https://www.origin.com/en-us/download. Once you download it, you'll need to associate it with your purchase of the game, perhaps an email address you used with your coupon.
If your copy is authentic, it's possible it was disabled. At the time of your question, Maxis developers were making many improvements to SimCity and may have disabled the Region Wall as they worked on it. Try again now, I have been seeing it working in my copy this week.
That said, the Region Wall is useful for sending a message to a player not playing simultaneously since the messages aren't delivered until the user loads a city in that region. Otherwise, Origin Chat is good for messages to simultaneous players.