Unfortunately, the Lithium Ion batteries used in laptops do shut themselves down after 300 or so charge cycles. This may be what you are seeing.
However, first thing is to go to
support.dell.com and enter your Service Tag number from the bottom of the computer. Then see if there is a bios update for your computer. I know it doesn't sound like it would matter, but it does. If there is one available, you can click on it and click on "Fixes and Enhancements" (or something like that) to see if the fix addresses a battery issue. If so, I'd give that a try.
Good luck,
WallyH