DC Jack diagnosis:
1. Test power adapter for output voltage. Bend the power cable in various directions while doing this to be sure that there is no broken conductors in the cable.
2. If power adapter is Ok, connect it & see if the power LED on the laptop will glow when you jiggle the power connector in various directions. If yes, then the DC jack might be loose or damaged, & need to be either re-soldered or replaced.
3. If not, then disassemble the laptop. Remove any components that attach to the laptop's motherboard first (e.g. battery, hard drive, RAM, wireless card, optical drive, ... etc.)
4. Next, remove the keyboard & the LCD screen.
5. Finally, unscrew all screws that hold the upper cover & lower cover together so that you could gain access to the motherboard.
6. Inspect the solder points connecting the DC jack to the motherboard. Make sure that none of them is loose. If any, re-solder them.
7. Inspect the center pin in the DC jack. Make sure that it is not broken or loose. If it is, then you might need to replace the DC jack.
8. When you are done, re-assemble back the laptop.