You must try putting the ac-dc adapter disconnect the battery. If the power laptop work the system is o.k 2) try to put again the battery start again if the system work gread. If doesnt. proceed as: disconnect the power adpater+battery and proceed to make a HARD RESET:Hold THE POWER BUTTON BY 60 SECONDS, and try again putting the adpater+battery and try again. this will be fix it the problem.
However if the problem remain. test this a) measure the ouput for adpater see the indication voltage will be 17.2 -18 vdc use teh VOM, if doesnot have any voltae the adapter is faulty. open and repair or replace b) test the battery with the software diagnostic coming with the computer or download from the www. dell.com and test the battery condition.
However the power supply can be faulty inside, some capacitor, diode, resistor, can be open or faulty or short. Test the fuse or c. breaker, insider( the adpater has a fuse inside your must open carefully).
God bless you