Why wont my kodak m1063 turn on?

My kodak has been in my closet for probably bout couple weeks without using it. i went to turn it on a couple days ago and it wouldnt (Assumed it was dead) so i plugged it in and pressed the on off button (usually the light comes on). Well this time it didnt. so i decided to let it charge over night and when i awoke to it the next morning it still wouldnt work. But i did notice when i plug it in, the lcd screen faintly lights up and goes away when i unplug it? any suggestions on what i do or whats the problem with it?