It's working fine when on mains power, but the battery isn't charging; on hovering the cursor over the battery icon, it's telling me "0% available (plugged in, not charging).

Is the battery dead; it shouldn't be as it's a new laptop? Is there anything else I can try to fix the problem?

Dileep, December 2010

That may be true for Nickel Cadmium (NiCd) and Nickle Metal Hydride (NiMH) batteries that do need to be constantly run down to preserve their life but not true of the Lithium Ion (LiIon) which are desiged to be constantly topped up from being hardly run down. That's why the latter were so good for being installed in mobile phones and laptops like this.
If its a new computer from Dell it'll have the 6 cell LiIon battery in it. If it has no charge that the battery is faulty or the charging circuits are faulty. Get on to Dell to get it repaired under the warranty.

Stephen, January 2011

most people ruin the battery by not letting it discharge,they plug the laptop into mains all the time,
so your battery may indeed be faulty

mm, December 2010