Chances are it is the power jack, but take a careful look at your power adapter to make sure. Replacing the power supply is the easiest way out of this, if that is the problem.
On most laptops, the power jack is soldered onto the system board. Manufacturers and many computer shops will tell you that the system board needs to be replaced... which pretty much means a new laptop.
It
can be fixed, though. What needs to be done is the laptop needs to be completely disassembled, a new DC jack needs to be purchased, the old jack needs to be desoldered , the new one needs to be soldered and finally, the laptop needs to be reassembled. This work is above and beyond what *most* people can/will do. Here are some
general instructions.
The solution is to find someone who can resolder it for you. True, it is something you
can do yourself but if you don't have experience soldering, I wouldn't start out with a laptop.
There's also a slim possibility that your power jack is modular. A modular jack plugs into the board and is held down by a clip or screw etc.. it can be replaced without any soldering work. 98% of laptops aren't like this, but it is worth checking out. Even the act of taking apart most laptops is a monolithic project for the average person, but a modular DC jack will be much more realistic to replace than one soldered onto the board. Some Sony, many IBM and some HPs, for example, use modular jacks.