When did you have the battery replaced? Was it recently or over a year ago and now the battery is not working?
If this is not a recent replacement, you may have an issue with a dead battery for a variety of reasons.
Battery run-time will vary as you use your laptop daily. One days reading may be different than another's due to the different programs you may run on the laptop or the hardware you open. Setting your computer to battery save mode will help to begin with, but there are some other major factors to consider.
WiFi and video streaming use up a lot of battery watt hours, so reducing the use of these two features by battery power will help lessen the drain on the battery. Best to use AC/DC power when doing these two functions.
Save your overall battery life by removing the battery while using the AC/DC Adapter since the battery will continue to drain while in use and the adapter will continue to charge as it drains. This is not good for the battery. Some laptop may allow you to turn off the battery so the laptop will not try and use both the AC/DC and battery at the same time.
Condition your battery once a month with a full discharge and charge to help boost the battery cells and allow them to remember how to hold the best charge they can. When you do not do a complete discharge and full charge, called shallow charges, not all of the cells get conditioned and eventually some of the cells will lose their ability to hold full charges.
Laptop batteries will last 500-800 charging cycles or 18-24 months on average. Shorter if you use the battery all time and do not remove the battery when using AC/DC power. Once the battery is charged. remove the charger so you do not over charge the battery.
More battery tips and a Dell replacement battery link:
http://www.batteryfuel.com/faq1.html
http://www.batteryfuel.com/laptops-dell.html
http://www.batteryfuel.com