Fixing the "could not activate cellular network" problem on iPhone

This problem randomly hit recently.  Phone calls worked, so did wifi.  But I could not get on the cellular data network with my phone.

Forums suggested the following hierarchy of fixes:

1. Switch to airplane mode and back
2. Soft reset (hold sleep/wake button until red slider appears and power off)
3. Hard reset (hold sleep/wake button AND home button until Apple logo appears)
4. Reset Network settings (you lose all wifi passwords): Settings -> General -> Reset -> Reset Network Settings
5. Restore phone

I did 1-4 without any luck and wasn’t thrilled with the idea of #5, but it turns out the fix was easier than that. 

Fix: using a paperclip, I popped out the sim card tray, dumped out the sim card and then put the card back in the tray and the tray back in the phone (see video for play-by-play).  Success!