Problems restoring IPhone 5

I just got my IPhone five battery replaced and when I got it back, It said that I had plug it into ITunes. When I did it told me that I had to restore and update so I did. I noticed that after it finished extracting the software, the serial number that was previously there became n/a but the phone proceeded to show that it was restoring. When the bar was full (Like it was finished restoring) the screen turned black and the phone told me to plug back into ITunes. The computer said that I had to restore and update ago so it just went back to where I started off. I've retried many times to see if I did something wrong and I can't turn it on at all because the only option it gives me is to plug my phone into ITunes. Is there anyway to fix this?