This suggests to me that you need to check out the AC adapter, and see if there is an intermittent short. In otherwords a break in the wires.
AC adapter unplugged from laptop, and power, remove the AC power cord from the body of the AC adapter.
Use a multimeter set to OHM's, (1K), and connect the Positive (Red) probe lead to one of the flat bladed prongs, in the power plug that plugs into the surge protector.
Touch the Negative (Black) probe lead to one of the holes in the plug, that goes into the AC adapter 'body'.
Keep going from hole to hole, until you get a reading.
Now have an assistant gently wiggle the power cable, and see if you get an intermittent reading.
Do the same for the other plug's flat bladed prong.
Intermittent reading means replace the power cable, or if more feasible, the entire AC adapter.
Power cable proves to be fine, move on.
Plug the power cable back into the AC adapter. Plug the AC adapter into power.
Using a multimeter set to DC Voltage, touch the Positive (Red) probe lead of the multimeter, to the center hole of the plug that goes into the laptop.
(If just a symbol, the DC Voltage symbol is a dotted line over a solid line)
The Negative (Black) probe lead, touches the outside cylindrical metal shell, of the plug.
Have an assistant gently wiggle the cable, and see if there is an intermittent reading on the multimeter.
(Reading should be 18.5 Volts DC)
[There are Analog multimeters which have a scale, and a needle, and Digital multimeters that just have a digital readout.
If using an Analog multimeter the needle will drop towards 0.
If using a Digital multimeter the readout will drop to smaller numbers, or 0 ]
AC adapter checks out? Go on.
The port on your laptop where the AC adapter plugs in, is the DC Power Jack.
AC adapter unplugged from laptop, Battery removed.
Take a pencil, and gently use the eraser end to see if you can wiggle, the center pin of the DC Power Jack.
ANY perceptible movement means a problem with the DC Power Jack.
The GOOD news is that the DC Power Jack, is NOT soldered directly to the motherboard.
It slides down in a Channel on the outside edge of the Base Enclosure, and has a wiring harness coming from it.
The end of the wiring harness has a plug, that plugs into the motherboard.
The HP part number for this DC Power Harness is HP 600630-001
This is a link to a free Service Manual from HP Support,http://h10032.www1.hp.com/ctg/Manual/c02627955.pdf
Page 73 is for the Power Connector Cable.
No damage to the DC Power Jack, and the harness is not slightly unplugged?
Now you have real problems.
You have a bad Power MOSFET,
B) Power MOSFET:http://en.wikipedia.org/wiki/Power_MOSFET
However it doesn't take a rocket scientist to replace. (Sorry Gort)
These SMD's use a J-lead contact. Simple unsoldering, and soldering.
(Better be fast though as you don't want to overheat a power transistor. Better be good, because you don't want any cold solder joints)
For additional questions please post in a Comment.