My iPhone 4S says 1% all the time?

I was using my phone yesterday a lot, and i had realized it said it was on 1% battery life, but I never got alerts for it being low or anything. So I plugged it in the charger and it said it was charging, but as I was using it I noticed it still said 1%.

So I left my phone alone for a long while so it can charge, I come back to it and it still says 1%! I unplugged it and thought maybe it's just a phone glitch and when I unplugged it, it died, like it showed that wheel of it turning off. And I was just like "wtttfff."

So I put it back n charge and it shows that charge icon, but after some hours it never increased. So i let it charge all night, then it turned back on at 9am and it still said 1%!

I tried to restore it on itunes and wait 3 hours only to find it couldn't restore because of a system error. I have insurance on it, but I want to see if I can fix it cause I can't back anything up now and I have a lot of stuff I want on this phone.

Added (1). FORGOT TO MENTION this phone is LITERALLY not even a month old yet, I just bought it brand new.

You need to buy a new battery. You don't have to get a new phone or anything, but there's a problem with the battery. You should contact Apple and set up a repair for the battery. It probably leaked or has just been used up. Once you use a phone for a long time, the battery starts to wear down, yours might have done that all the way. You should not have to do a system restore, unless Apple says so after the repair is done. Hope I helped, and sorry about your phone!

It's a software glitch. Turn the phone off and charge the phone. After fully charged, turn it on.