I would tend to agree with the above. The green light shutting off on the power adapter/charger is most likely due to the fact that the battery can no longer hold a charge, therefore the adapter/charger will not move power through to charge the battery.
Would recommend a new battery. If that fails to solve the problem, purchase a new adapter/charger. Worst case is you have 2 new components to power your laptop - typically both are fairly inexpensive. Don't necessarily need to stick with Dell components, although I'm sure some may feel otherwise.
Good luck!