s5200 won't turn on after charging overnight

I have a semi-new s5200 that won't turn on after charging overnight.

I have charged it by plugging it to both my computer,anbd the wall charger.
All my camera does is have the recharge light blink.

I was using it for a while. One time I plugged it in,and it kept on turning on and stating that it had a low battery, before shutting off to charge once more.
It kept on doing this for a while. But it eventually charged and worked for a while, until I had to recharge it once more.

I am thinking a new battery is in order.

Welcome...Sounds like it has malfunctioned, Is it still warranted if yes take it back...

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Thanks

How old is the camera?