DC Jack or AC Adapter is the problem, have you tried another AC Adapter with the system. Boot the machine to BIOS and check battery info, you'll find information on that screen that will tell you if it's detecting an AC Adapter or not.
If the DC jack is ok then the computer would work with a new AC Adapter. When I say DC Jack I mean the jack where you plug the power brick into the system. These are known for getting broken on any laptop (except for the three prong style Dell used to use)