RE: Battery not charging,laptop not working withou adapter
In order, try
A new (or known working) Dell OEM AC adapter (many computer shops will have these and likely be willing to let you try one). If that works, replace the adapter.
If that doesn't work, replace the DC jack in the system (if you need a part reference, provide the full model number -- Inspiron N5110, 5531, etc.).
If the jack doesn't get the adapter recognized, the charge circuit on the mainboard is bad - replace the system board.