I have an Inspiron 9300, the battery hasn't been charging. The laptop works fine as long as I keep it plugged in. I've replaced the battery and the power supply. Is there something else I can try before looking into a Motherboard.
The Battery Icon should tell you whats up if you mouse over it. It should say "Plugged In Charging", if it says "Unknown Adapter" it is getting power but doesn't like the adapter and won't charge with it.
Your Dell may be too old, but going to the BIOS with F2 on POST has battery and charger info as well.