My kodak easyshare m580 WILL NOT charge?

Ok, I'm severely pissed right now. I'm a college student and I recently bought an m580 kodak easyshare. when i bought it off ebay, I charged it up, and when I took it off the charger it would NOT turn on. I figured the battery had gone bad, so I bought I new one not too long ago. It finally arrived only... show more Ok, I'm severely pissed right now. I'm a college student and I recently bought an m580 kodak easyshare. when i bought it off ebay, I charged it up, and when I took it off the charger it would NOT turn on. I figured the battery had gone bad, so I bought I new one not too long ago. It finally arrived only last week, and it was working just fine. It's brand new and had never been opened.

The battery was only half charged when I put it in the camera [which I found rather weird] and it died when I was in the middle of taking pictures.

I quickly put it on the charger and left it there for a while and checked it. It was only slightly charged when I looked at it so I figured it just took a REALLY long time to charge. so I left it there overnight and on until today after classes. I just took it off and it's DOING THE SAME THING AS BEFORE.

It WON'T turn on and will only do so when it's ON the charger. Now I know damn well the stupid thing can't be dead. When I have it on the charger, the charging light blinks...Maybe it's not actually charging, I dunno. all I know is that I'm seriously upset because I NEED this camera in order to do my homework.
Update: I should note that when I plug the battery in it says that it is fully charged.
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