When you finished story mode, did you close the game during the credits? The action that unlocks Open Mode happens after the credits, but you can skip them. Also, Open Mode will not unlock if you do Sterling's path.
The correct way to start Open Mode is to go to "new band" but the option isn't appearing for you...
And even if you've played the game once, you should still see a screen after hitting that button. The game is reacting like you've never played before. I suggest skipping through the beginning of the game (until you make your band) and then try "new band".
If all else fails, there is a cheat I can give you.