|I'd be inclined to double check the battery is correct for your model Dell. And presuming it is... verify your charger (ac adapter is actually working). Any prospect of borrowing an other charger/ac adapter to test with (ensuring it is definitely one compatible with your Dell)?|
Does the laptop work OK on mains power only; which means without the battery but your current ac adapter plugged in (and powered up of course)?
If it does work on ac-power only, then it points either to problems with the on-board charging ccts., or connector, or the battery itself (even though "new")?
A google trawl like this one below brings up more than a hits about the problem - and with that model Dell too...