My Iphone 5 wont turn charge

A few weeks ago the battery life icon of my phone stopped telling me however much charge I had left, it was stuck on however much charge the phone actually had before it was last turned off, I had to guess how much charge it had left, which meant my phone would run out of charge regularly. When I started charging my phone after it ran out of battery it would keep restarting while on charge, and if i was on the phone the screen would corrupt and the phone would turn off, this would stop after like 30%. Now my phone doesn't even get past the apple logo when I put it on charge, the apple logo appears then the phone turns off then it reappears and it just does this. It wont turn on or connect to my laptop. I'm not sure if this is a software problem or the battery has broken, I can't contact apple support because I cant get the serial number and there is no apple stores nearby. Has anyone experienced any problems like this and know how i can fix it? I also have photos on my phone that i havent backed up which i dont want to loose.

I have an iPhone 5 8gb with ios 8.1.1