Settings>about phone>status>sim card status
Now when your on that page turn off your wifi, give it a min or two to transfer the connection to mobile.
Do you have something under mobile data network?
Any app on your phone should have data access if its working properly.
you can do a test if its working properly by turning off wifi and trying to load a web page like google.com
Its possibly you have data turned off
Settings>connections>data usage>mobile data
Make sure this is on, if its still not working then your issue could be more serious or from your network provider.
It may be that your access point is not set up correctly. Contact your provider for the details needed and then go to:
Settings/ Connections/ Mobile Networks / Access point names/ Add
and fill in the details provided (normally, not all fields need to be completed)
While you're at it, go to
Settings/Connections/ Mobile networks/ Network operators
and make sure that Select automatically is selected.