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.
Power MOSFET Wikipedia the free encyclopedia
More information using a prior solution,
Dv6000 power light does not come on any more
Check the links given.
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.
AC Adapter For Compaq Presario All in One CQ1 1225 Desktop PC Charger...
Just my thoughts..........