DC Adapter/DC Jack for Inspiron 5100

Good evening...My Inspiron 5100 no longer turns on with the AC Adapter.  Assuming it was the adapter, I purchased a new one, but the inspiron still will not turn on.  The Inspiron works with the battery, but I cannot re-charge it.  Both AC Adapter show a green light when plugged into an outlet, so I assume they are working fine.

 

I also assume that I need to replace the jack when the adapter plugs into the Inspiron.  Is this something I can order from Dell and replace myself?

 

Thanks in advance...LC