Well, I didn't upgrade from a previous build and had the No SIM/NO Data issue. After several hard resets, the SIM was detected, but I still had not data connection, although my phone showed an LTE signal.
I tried to roll back to 8.1 which was borked for some odd reason. I then hard reset again, and 8.1 was back. I upgraded to 10 from that point, and chose to do a fresh install as opposed to restoring a backup. Then I went into the Settings and Extras and selected Access Point. I put the APN info in, which I had tried several times before, and I was then able to get a data connection.
So, I hard reset again to restore my most recent backup, but it had been overwritten. I chose the one that was there and the no data connection issue returned. I hard reset AGAIN and chose my backup from December and all was well, minus 3 months of text messages.
So, if you have this issue, do a hard reset, a fresh install, a hard reset and restore from a backup. Oh! And, do not select Backup the first time around or your most recent backup will be overwritten. Hope this helps someone.
Lumia 925 also on T-Mobile.