Controller Problems, Need Help!

I just ordered a Jungle Green PS3 controller from Amazon and got it today. I opened it up, threw away the package and started charging it. This would be the 7th or 8th PS3 controller between my brother and I. So I got on MW3 (ugh, I know.) because my friends wanted me to play. I unplugged my new controller and start using it. Right away I could tell that there was a delay when I would press down on the dpad and analog stick while n the menu. The right analog stick is messed up, it seemed almost twice as sensitive compared to the left analog stick. Also, every 2-3 minutes the "Controller needs to be charged" message would pop up. I know for sure I charged and when I went to the XMB, it showed that my controller was fully charged but that message still kept popping up. I've been looking all over google trying to find a solution or anyone who has the same problems but couldn't find anything. So I figured I'd see if one of you guys might have experienced the same issues I am having and know a solution.

I've tried turning it off and back on, plugging it back in, using the reset button on the back of the controller and shaking it violently hoping it would fix itself. I would like to add that I did try using my old controller after testing out my new controller and it the old controller worked fine. Like I said I had 4 sixaxis controllers and I think this would be the 4th dualshock controller I've owned. I never had problems like this when I first started using them. After several months, the analog stick would mess up and it would make my character walk forward without me pressing anything. Also, like my last controller, the X and Square buttons would get stuck when I press them (not because of any drinks or food). I've never experienced all these problems with a new controller before.

Any Amazon users here? If there is no solution to fixing it, does anyone know if I could still return it or exchange it even though I don't have the packaging it came with?