Why won't my iphone 4 let me touch the screen, and why does it keep restarting?

I had this phone for 10 months now.
It's been restarting for about 20 hours now.
It won't let me touch the screen, it stays on the lock screen, that says enter passcode.
I connected it to my computer, synced it ' and it worked fine again for a few hours.
Then a couple hours later, it wouldn't let me put in my passcode again.
But NOW, it keeps restarting over, and over again on it's own.
I tried to back it up, restore it and sync it to my computer, but it keeps turning on and off so it doesn't stay connected, so the process isn't able to complete and It still won't let me type in my passcode.
I don't know what to do.
How do you stop it from turning on and off?
How can i fix the screen again?
By the way.
*It has no water damage*
Anybody know how to fix this?
Please, any suggestions?

I think its time for an upgrade

Download any new software

He can't touch it

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