Verify that your AC adapter is the one that was supplied with your laptop. It should be a Dell 65-Watt adapter with a part number of TR82J. This number should be listed on the large rectangular portion of the adapter. Once you are certain you are using the proper power adapter, you can continue.
When you plug the power adapter into your Dell Inspiron 1501 laptop, it should immediately be recognized by the computer and the battery should begin to charge. If this fails to occur, a number of issues could account for the problem. You must make sure you are using the proper adapter, that it is assembled properly and that it is connected to a live power source. Once all of those pieces are in place, your Inspiron will recognize the charger.
Make sure that the power cord is plugged properly into the rectangular portion of the power adapter. The two are not permanently fixed and they can come apart if tugged.
Plug one end of the charger into your laptop.
Locate a free wall outlet and plug a lamp or another electrical item into it to ensure it is functioning properly. If the outlet works, plug in your power adapter. The laptop should recognize it immediately and begin charging.