Can you take out the memory and data in an iphone and put it in another iphone?

I might have to buy another Iphone because mine won't turn on and I didn't back it up on my computer because everytime i try to sync my phone to itunes it shuts off the first 3 minutes. I'm going to try to get my computer fixed. But right now It's not. I really need to keep all my files in my phone but right now, the only solution I can think of that will get my phone to turn back on is to reset its factory setting, and again, thats not really an option for me.

how it looks when i try to turn it on: it shows the silver apple, looking like it's about to turn on when BAM it glitches off. It keeps on doing that.

i tried to press the home and lock button at the same time for ten seconds but it tells me to hook up to itunes which i'm doing and it's still not turning on.

Is there a way to convert and the data from my old phone to a new one? Please i need help.a lot of my work and school work is on it and a lot of personal stuff is on my phone and i have horrible memory so i can't really restart everything.

Your only hope was having backed up your iPhone on your PC and since you said you never synced your iPhone to your PC there's no other way to recover your data. You can try to jailbreak your iPhone in this state and hope it fixes everything. Jailbreaking won't erase anything