Connection Failed

I’m trying to sign into NFS HOT PURUSIT 2010 on my Xbox 360 but when I enter my account details into the create account menu it gives me an error code and then says connection failed. I already have an existing account that I want to sign into the game with but it gives me this error saying connection failed. Also I should note that I also have NFS MOST WANTED 2012 on my Xbox 360 as well and it signs me in just fine in that game. If anyone can help me fix this issue with Hot Pursuit I will really appreciate it. Also I should note that I lost my game case so I have no product key to use.