Two friends and I also use roughly the same model of laptop (they all use the same charger, so I assume it's the same one you are using).
Try looking into the following:
1. Try finding another laptop that uses the same charger and/or battery. Try their battery in your computer. If it works then the problem is probably your battery.
1. Look into the end of your charger. Is there a tiny pin in the middle of it? My friends and I haven't quite figured out exactly why, but if the pin is broken, bent, or even completely missing, the laptop doesn't charge the battery properly (probably some safeguard implemented by Dell to prevent people from buying other chargers)
2. Does your charger charge the other battery properly?
3. If said laptop also uses the same battery, try putting your battery into the other laptop. Does it charger properly? This might be related to the pin thing, but this time maybe an issue with the motherboard side not accepting the pin.