Hi!
Could you please update the post with some more information, like whether or not the battery was replaced before and if you can confirm that the AC adapter is working properly.
As a first step I'd recommend that you check your settings in the Dell Power Manager app. You can find it by typing its name in the start menu. This app comes preinstalled on most recent Dell laptops and it has a setting that does not let the battery charge if certain conditions are met. You can look at [http://en.community.dell.com/support-forums/laptop/f/3518/t/20015923|this forum post from Dell] to get more insight on what I mean.