iOS 7 update failed - stuck on Connect to iTunes
When your phone gets stuck trying to update, it usually means it has way too much data in it. For a good average update that's takes at least 20 mins, you'll need to have at least 2.5 GB. Your phone has gotten stuck because it had way too much stuff in it, and it can't continue. 

My solution: restore the phone. There is way too much data inside,and it will stay that way unless something happens. This can be a good and bad thing. If you had some stuff on iCloud or some storage, you just might restore your apps and everything else. But if you don't, let's just hope you had nothing important in the phone, because it might just go down the drain. Besides you are left with no other option, right?

I hope this helps. If you find a better way, please use that way instead of this way. I hope you are able to fix your phone.