We might have a very similar issue, I also don't have a solution (yet).
My phone does not connect to 3G, only 2G and LTE.
To check if you are in the same situation:
then play a little with the settings there... (for example try 3G only).
see if you get any positive things out of this.
(as a note: in some of the options I can connect to 3G, BUT I cannot make or receive any calls - internet is working though). You can choose a single option only (try each 2G, 3G, LTE and see what happens). However, I strongly suggest to keep a combination of 2, see the note above).
Samsung Galaxy S4 LTE - Stock, rooted KK 4.4.2
Samsung Galaxy S3 - rooted, S4 Revolution 40.0
Samsung Galaxy Tab 10.1 - rooted, Omni ROM
Xperia Arc S - rooted, AORP 4.4.2
Huawei P1 - rooted, RootBox ROM, JB 4.2.2
Desire HD - rooted, VenomROM - retired to pension/backup phone