Data Recovery- iPhone 6
 

My iPhone 6 turned off about 3 days ago and hasn't turned back on since then. I was just on vacation for five and a half weeks in Europe and I need the data on there- which hasn't been backed up since before I left, so it's not on the cloud or anything. If anyone has any ideas of what I can do please tell me. We've already been to the apple store which doesn't do data recovery and took it somewhere they recommended, but they didn't know what it was and couldn't do anything about it.
Even the diagnostics fees are crazy, but I think it might be worth it to pay if I must.

My phone did that, though it's an iPhone 4.
I left it on charge for an hour, took it off, held the home button and the sleep button together for 10 seconds and kept on doing it until it turned on.

I did that a few times until I took it to the apple store. Though the charge was at 98 when it shut off. How many of times do you think you had to do that?

I sat there doing it for about 5 minutes.
So the apple store couldn't fix it?

I'm not sure if this would be possible but I'm sure if you were desperate someone could take it apart and get the hard-drive (or whatever the substitute is on an iPhone) out.

The apple store couldn't, no. The best they could do is offer a replacement.

I've already had it taken apart. There isn't a sim card/memory chip in an iPhone or anything, so there's nothing to take out supposedly.