** UPDATE 8/14 **
I took the phone back to the guy who originally replaced the screen and he said that the charging port on the Lumia's are very finicky and he has seen them go bad many times. The kicker is that the charging port is directly linked to the network antenna, so when the charging port goes bad, the symptoms are exactly what we are seeing.
He ordered the part, replaced it the next day (didn't charge me because the damage could have been done from the screen replacement), and the phone is back to normal now.
If you're in the northern california region, he operates as Phone Hut in San Jose. I highly recommend him. He also fixed my sticky blackberry keyboard for $30.
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I've been in the same boat since yesterday. The screen cracked all by itself a couple of days ago -no really, i took it out of my pocket and the entire glass was cracked like a spiders web. I had the screen replaced, then after starting up, it got stuck in the airplane mode issue EXACTLY as you described. I initially thought it was the screen replacement guy's fault .....but after researching this, it seems like the problem has something to do with a hard reset AFTER the cyan update.
It definitely sees the SIM card because if I remove the SIM card, the error says no SIM present.
I tried Nokia Software Recovery, Retail, Hard Reset, Soft Reset, standing on one leg reset.....
Only thing I have not yet tried is THROWING IT AGAINST THE WALL!!!
I really regret spending another $250 to get the screen repaired!!!
Also have been very disappointed by the lack of support. I went to the Microsoft Store and they didn't even know who COULD fix the cracked screen. If MS wants to be a device company, they better have support figured out. This is not like OS updates they can just push out on you when they feel like it.
Just bought this POS 2 months ago and have had nothing but problems with overheating, lock screen issues, touch sensitivity is annoying when it thinks you clicked instead of swiped, can't attach a damn PDF to a reply email, WTF?!!
Fortunately, there's some good alternatives coming up. Counting this Craplet as a loss on the business books and moving on!
Looking forward to the new iPhone, can't be any worse than this!