if the battery is dead, could be as simple as bad dc adapter or dc adapter plug, you were right to check volts, but sometimes, correct voltage doesn't necessarily mean the right amps are flowing through. check the dc adapter cable, usually right near the plug (the dc plug that connects to the laptop). they tend to fray (usually not visible but underneath the insulation) because of awkward positions and pulling to the side, etc. if it's the cable, you'll find that moving the cable into different positions will give you some signs of power. sometimes the cable can look stressed at that point too. if you have a good feeling it might be the cable, and are okay at soldering, try ripping the cable up.
a busted jack is harder to diagnose, you have to make a direct connection onto the motherboard. I've only seen a broken jack though, and once was because the motherboard power jack was arcing.
if battery has charge, and laptop still isn't powering on (ruling out faulty dc adapter and plug) it's more than likely the mobo. components (besides power supplies) shouldn't cause power issues like this. you can try pulling components out to double check, though.
unless you're positive it isn't cable, i'd try the cable first, especially if you know how to solder.
