Why won't my iPhone 5 turn on?

I downloaded the iOS 7 beta and when iOS 7 officially came out I didn't download it. My phone was working normally until this afternoon when all of the sudden it wouldn't turn on. (It wasn't dead) so when I got home I plugged it into my computer and it wouldn't turn on or connect to iTunes. All it did was flash the apple symbol ever 4 seconds. So I put it into recovery mode and it connected. I tried to restore it and update to the real iOS 7 and when it finished extracting the software it said there was an error and it couldn't restore and update. Now my phone is also stuck in recovery mode. Does anyone know how to fix this?

Added (1). I had problems with my first iPhone 5 and got it replaced. This one is about 6 to 4 months old. I can't remember exactly

How old is your iPhone 5? You might have to get it looked at by Apple. Take it to the Genius Bar.

Turn off your anti-virus firewalls and try again. Then try another computer. If that doesn't work than it is the phone and it needs to be repaired.

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