Sorry to bump this topic, but I thought it's better to have one place to talk about "iPhone 6 Blue Screen of Death", also for people coming from a Google search (like me).
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That said, I'm encountering the same problem.
I had an iPhone 6 128GB running perfectly. No problems at all. Some months later the volume down button became faulty, so I decided to go to the Apple Store and they replaced it.
Full of joy (pff, how wrong!) I kept walking outside the Apple Store with a cellular connection to restore my iCloud Backup, but somehow my connection dropped all the time, so I waited a couple hours to go to my work place and use a more reliable Wi-Fi connection.
iCloud restore went good. Everything was fine. Thank God, I got a perfect refurbished iPhone 6 128GB.
Went back home 8 hours later. I connected my iPhone 6 to my Wi-Fi network which stands right in front of me, so I had full bars.
All of a sudden, after some minutes of messaging, Wi-Fi bar went from 3 to 1 bar and iPhone became unresponsive.
Cool, it blocked, let's restart it with an hard reset (standby button + home button).
iPhone restarted and....wow, that's magic. My Wi-Fi icon went GREY and I couldn't activate it.
Ok, it might be a restore problem (I thought), let's restore it entirely through iTunes in DFU (yeah, it was totally unresponsive again).
"Waiting for iPhone..." said iTunes. It kept waiting for 5 minutes. Then threw a 4003 error. Tried again, 4004 error.
I was having an hard time. I had just got a brand new iPhone 6 128GB by using my WARRANTY and I had got a non-working iPhone. Nice. So I waited a couple minutes.
I decided to try again. Restore went through. Wi-Fi was working again. NICE! Backup restore went through too.
Everything was working perfectly! Oh wait, the Wi-Fi bar just went to 1 bar. Oh it's blocking again. Unresponsive. It restarted itself a couple times. Blue screen. Restarting. Blue screen again. Restarting. Stuck again. Restarting. Restarted and working again.
As of NOW I can use my iPhone, but whenever I try to open "Settings->Wi-Fi" the Settings panel crashes.
"Settings->General->About" shows me a N/D Wi-Fi address, meaning that the internal wi-fi chip is not talking to the motherboard. Cool. I will surely return it to the Apple Store tomorrow. And no, I'm not going to take any appointment, I have no time for that (first appointment available in 3-4 days).
P.S.: this seems to be very similar to the iPhone 4S grey Wi-Fi problem. Whenever the iPhone got hot it stopped working.
Have a good day.
t0r