Set the phones mobile data to CDMA only and reboot, then use Speedin07si's method to reset the radio, once done reboot again.
Most ROMs i tried usually has data not working when its set to CDMA/EvDO/LTE. And also.
Search the Q&A forum regarding issue's others had on that ROM, if you cant find the problem others have that you have.
Look for it under the ROM thread. If it isn't there either THEN post in the Q&A Section.
Hopefully a moderator can move this thread so you don't have to make a new one.
Samsung Galaxy S III
Carbon Rom 1.7
Stock AOSP Kernel
Epic 4G Touch
SlimRom Build6 / Touched By Galaxy S 4
Agat Kernel+Recovery 1.3.0 for jb
TWRP 188.8.131.52 for AOSP ZAPPed Kernel