NEED HELP:( iPhone 4s stuck on Apple Logo

I recently purchased an iPhone 4s from a guy off of FB, he said it only needed to be connected to iTunes. I connected it and it was in recovery mode but would not restore, I kept getting (error code 21). Come to find out the phone needed a new battery, so I purchased and replaced the battery. Then when I went back to try to restore it again there was no error code, but after it restored it wouldn't fully come on. It keeps getting stuck on the Apple Logo, I keep trying to restore and update it but haven't had any luck yet. A few times now when I have restored it, it has said to activate the iPhone with the original account it was set up with and then the phone will turn off and go away. Now I have tried repeatedly to get ahold of the man I bought the phone from but he won't answer me. So now i'm stuck with an iPhone that won't turn on and i'm not sure what to do! Someone please if you have any ideas of what to do, please help me!

Thank you.