You could remove the Sim card very carefully after the phone is off. Then put it back in and turn on the device.
See if this helps.
Also the below link says for an iPhone 5 but its the same for the 6 and 6+
This link may also help.
This was one of the steps that I tried when trouble shooting the issue. I had no success with it.
However, I was able to get my phone back in a working state! What I did was turn off iMessage and Facetime, then reset the network settings (I tried this previously also, with no luck). This re-enabled the LTE on my phone, but I was still unable to receive texts and calls. I reset the phone again, and that did the trick to enable the full functionality.
Thanks again for everyone help!