Try doing a reboot by holding both the power and home buttons until the apple logo appears and it restarts, ignore the red slider if that appears.
If that does not solve the connectivity problem:
Settings > Airplane Mode ON, Do Not Disturb ON
Power down for 5-10 minutes
Settings > Airplane Mode OFF, Do Not Disturb OFF
See if that helps, if not you may need to backup the content and restore to factory settings and then restore from the backup you made.