Have you noticed that your cursor no longer moves in the save select screen?
There’s currently an issue that occurs when you click to Continue your game in Co-op, then immediately Quit to the Main Menu and create a New Game. Going through these motions too fast causes the game’s cursor to stop moving.
Speed was your enemy here! If this happens to you, just close the game, and re-launch it. Then, take your time and be sure to press New Game!
If in the future you hit Continue again, just go back to the Main Menu and wait a couple seconds before pressing New Game. Take your time and everything should work properly!