Sounds like you need a new battery- if possible, you should try turning it on with it plugged in, if it works fine, then it's definitely the battery. If not, could still be the battery, but could be other things as well, however it's 90% probable it's the battery.
You can get the battery [http://www.amazon.com/gp/product/B003F3ZBKI/ref=as_li_ss_tl?ie=UTF8&tag=rab777hp-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=B003F3ZBKI|for less than $10 here]. Definitely worth getting a new battery and seeing if it works fine then.