No Simcard installed - iPhone 5
This is often caused (but by no means is this the only possible cause) by a badly fitting sim card, or sim tray.  That doesn't explain how a hard reset would make it work though.  I would see if you can borrow a friendly sim and tray from another iPhone 5 users, and see if you can get the same results, or improved results, by using different combinations of sim card and tray.  When you get one that works, run away and leave your friend with the duff bits ;)