4s keeps crashing and then showing low battery then kicks in when it wants to and shows full battery.

Hi....this is so frustrating for me, So if anyone could help would be great.

I have an iphone 4s 16 gig.

I have restored it as it was crashing all the time, so i have done a upgrade to 5.1.1

My fault is i can leave my phone in to charge all night anyway at full charge i could press a button then the phone goes of and shows the battery indicator showing it dead...then sometimes it kicks back in and shows it fully charged, or i have had it were i just plug the charger back in and it kicks back up showing the right charge..I have nothing on my phone other then the factory setting and still keeps crashing?

Do you think the battery is faulty??

History the phone got water damaged about 6 months ago and besides getting the screen being replaced the phone as been working for 6 months until now?

Can someone direct me as to what i need to spend next to get this phone working again it is so frustrating as the money i paid for this.....i got screen replaced and water damaged so warranty is void i guess.

Thanks

Toby