I had a similar issue when I flashed to a Carbon Rom nightly (I think 9/10). Anyway try sending an MMS message to someone. If it can get through, 4G LTE works. You are having an issue with 3G and/or CDMA. Now I tried these steps
that SlimSnoopOS suggested. None of them worked for me, but hopefully they work for you.
If they don't I'd flash back to complete stock. If data is STILL not working something that oddly worked for me was TriangleAway. My binary flash counter had been tripped and after running TriangleAway my mobile data came back. Not too sure on that one...