Why doesn't my game center work?

Please can anyone help me?! I have an iPod touch and I cannot sign into game center on it. Game center doesn't even come up in my settings as an option to click on. I have version 6.1.6 and whenever I go onto the game center app, it tells me to sign in with my Apple ID and password. I do so and it takes me to a page, tells me it's loading and then comes up with a blank page! I've tried restarting, changing the date, taking the case off all that malarkey and still nothing! Any one have any ideas? Suggestions would be greatly appreciated, thank you!