I had a very similar problem with my old iPhone 5. Long story short: I had a Black 16GB iPhone 4S, the screen got cracked and the Wifi Chip broke (Under settings the Wifi option was greyed out). I payed $60 for an issuance replacement by AT&T (Asurion). Each "refurbished" iPhone 4S they sent me had problems (they sent me 5 iPhone 4S's each one had a problem), so they felt bad and sent me a Space Grey iPhone 5 64GB. Unfortunately for me I quickly discovered there was a battery problem, and I ignored it due to the fact that I was given a great upgrade. It came to the point where it was charged at 100% and would it last about 2 hours maybe less. So, I replaced the battery with one from iFixiT, and after replacing it the phone wouldn't charge or power on, even after putting the old battery back in. Anyways, I called AT&T one last time and they said they were so sorry for the trouble, and to show their graditude they sent me a brand new Space Grey iPhone 5S 32GB (to ensure I wouldn't have any more problems cause its new). Ok it's a rather "long" story Lol.