Anti-Static wrist strap connected to ground source, and your wrist;
1) The jack your AC adapter plugs into on the motherboard, is the DC Power Jack.
Motherboard out of case, power to motherboard, take your multimeter and see if you are getting 19 VDC at the DC Power Jack's positive solder joint, on motherboard.
The center pin of the jack is Positive. (The inner cylindrical shell is Negative)
Follow the DC Power Jack's positive pin from the Center of the jack, to the motherboard.
You probably won't be able to touch your meter's Positive (Red) probe, to the DC Power Jack's positive pin under the jack; so touch it's solder joint on the opposite side of the motherboard.
(DC Power Jack should be soldered close to the motherboard, is why)
Of course also touch the Negative lead, (Black probe), of your meter, to the Negative, (Ground) solder joint for the DC Power Jack.
Getting 19 volts DC?
See if there is a cracked solder joint, for any of the DC Power Jack's pin connections to the motherboard.
ANY perceptible movement of the DC Power Jack on the motherboard, indicates a bad power jack, and may indicate a broken/cracked solder joint.
Center pin of DC Power Jack is loose? Bad DC Power Jack. Replace.
2) DC Power Jack is determined to be in good repair? No cracked/broken solder joints?
The next components in the power circuit on the motherboard, leading From the power jack, are P. MOSFET's.
3) The last thing that concerns me, although I probably should have listed it first; is the AC adapter you are using.
Concern is that it doesn't have the 'intelligent chipset' that matches the Compaq CQ1-1225 All-In-One desktop PC's circuitry.
A) AC adapter (Charger) is bad. Use a multimeter, and check it out.
[ DC Voltage. Test plug of cable that plugs into laptop. Positive (Red) probe lead of multimeter, to Center Hole of plug on AC adapter. Negative (Black) probe lead touches outside cylindrical metal shell. You should read close to 19.5 Volts (DC) ]
AC adapter checks out OK?
B) DC Power Jack is bad
[The DC Power Jack is the port on the laptop, that the AC adapter plugs into. On laptop may be marked DC_IN ]
Damage to DC Power Jack prevents laptop from charging, or running strictly off of the AC adapter.
Battery removed take a No.2 pencil's eraser, and see if you can gently move the Center Pin, of the DC Power Jack. ANY perceptible movement means replacement of the DC Power Jack.
The pin itself may not move, and the entire jack moves. The good news is the DC Power Jack is not soldered to the motherboard. It is soldered to a separate, therefore replaceable, small circuit board,
Looking at the view on the right, note the pins sticking out. You are looking at the back view, and the jack is laying on it's side. The pins go through the laptop's motherboard, and are soldered to the motherboard.
Where the pins are soldered to the motherboard is a solder connection. Commonly referred to as a Solder Joint.
Plugging in, and missing the hole of the jack, can cause the AC adapter plug to damage the DC Power Jack, by bumping into it.
Bumping into the plug of the AC adapter, while plugged into the DC Power jack, can cause damage to the jack.
Can cause cracking of the above mentioned solder joints. This leads to an intermittent contact, and eventually no contact, of the DC Power Jack TO the motherboard.
In this case the solder joints are just re-soldered.
Damage to the body of the jack itself means replacement of the DC Power Jack, or replacement of the USB/DC Power Jack circuit board, itself.
(Unless you, or an acquaintance can un-solder, and solder real well, the option may be to just replace the USB/DC Power Jack circuit board)
DC Power Jack proves to be OK?
Problem is one, or more Power MOSFETs on the motherboard. These determine if the Battery needs a trickle charge, or a full charge, or no charge at all. Also determines if the laptop is to just run off of the AC adapter, and not the Battery.
This example is for HP Pavilion dv6000 and Pavilion dv9000 series of Notebook PC's. You can use it for cross-reference information. (Location of the Power MOSFETs on your laptop's motherboard. General idea of what they look like ),
first is the ac adapter hard to tell if its working or not
even if green light is on, it could be the end that plugs into laptop
next is the dc jack , take a toothpick or something
and touch the pin inside the jack where you plug the adapter
if this moves just a bit, the pin is broke , a new dc jack is 5 bucks on ebay or more, but youll have to take apart to install new jack
first you would try the least expensive
make sure your ac adpater works
the plug could be bad on the end
next is the pin inside the dc jack where you plug it in, if the pin moves just a little , you may need a new dc jack sold on ebay cheap
make sure the battery is out when testing