Replace the battery with a new one.

Is the battery issue something that just happens?  OR is there something we did to cause this?  How long do batteries typically last in a netbook?  My 13 year old tends to leave it on and unplugged and the battery runs out often...could that be the cause?

Yes, that will stress a battery.  Lithium ion batteries generally last 1.5-2 years -- if it's been run down often, the lifespan is reduced.

don,t buy a dell next time

I've been getting that error ever since my DCP has been having errors. Can they be related? Once the DCP starts working again the batt charges fully and seems fine. It keeps giving me errors about my AC cord being the wrong one as well.

Try a new Dell adapter - if that doesn't solve the problem, then the issue is with the power jack or mainboard itself.

The adapter is probably ok.  I would recommend a new battery.

I to have a dell inspiron Mini 10, and the same thing that is happening to you is happening to me. But the thing is, with my computer it IS charging the battery reguardless. I dont know what this is about but it is driving me crazy!!