iPhone can't run apps due to notifications.?

[Joh1]

My iPhone 5 can't open snapchat. What happens is I open the app then a nonstop cycle of notifications will appear saying:
Connect to iTunes to Use Push Notifications
"Snapchat" notifications may include alearts, sounds and icon badges.

I've tried rebooting my phone, turning off notfications, and I tried syncing it but my phone won't sync to my computer. Help!