With a Dell laptop, the most likely components to fail are the moving parts inside the computer. The longer you use your Dell, general wear and tear may take its toll at some point in time. The Inspiron laptop adapter may also fail, but since it has no moving parts, it is a bit harder to determine if the adapter is faulty.
Random power surges are common indicators that an Inspiron laptop adapter is faulty. If your laptop does not boot up or shuts down without reason, you could have a malfunctioning adapter. If you experience these problems it would be advisable to buy a new Inspiron laptop adapter to see if the situation is remedied. It is never a good idea to continue using an adapter that you suspect is faulty as it could very well damage the components inside your computer. If your Dell operates fine using battery power, then the cause of your problems are most likely the adapter.
A worn adapter cable could also prove problematic. If your Inspiron laptop adapter is showing signs of wear on the cable or the transformer you should replace it with a new one asap as it poses a fire hazard. If you notice that your battery is failing to charge all together, the cause could very well be a faulty adapter. Again, buy a new adapter as the one you are using is most likely to blame for a non-charging battery.
Of course you could always take your Inspiron and its adapter in to an authorized Dell repair centre to have the problem professionally diagnosed, but be warned that even a diagnosis is not free. If you happen to know someone who uses the same Inspiron laptop adapter that you use, consider asking to borrow it so that you can see if it works on your computer.