Without taking time to read 100% of every post... do you have a volt meter? If not, they are very cheap these days and learning how to use one to diagnose electrical issues saves TONS of time. I would suggest checking the output of the computer's power supply. There is a label on the power supply that shows you which side of the power supply plug is ground and which is voltage. If you have no voltage at the output of the laptop power supply, the power supply is bad, not the motherboard. With that many computers around, are you CERTAIN you have the correct power supply for THAT laptop? They sometimes have circuits that verify the correct power supply is connected and if you plug-in the wrong power supply, you might get nothing. Also, depending on how the battery is being used, if there is no battery in the laptop or if the battery has failed as a complete short circuit or as a complete open circuit, that might prevent the laptop from starting also. When the laptop is connected to its power supply, it's possible that a battery with a problem could prevent the computer from powering up.
The label on the power supply will have a little graphic with what looks sort of like a "C" surrounding a dot right in the center of the "C". The "outside" of the "C" shape will have a line leading away from it and it will be labeled "-" or "+" or possibly "gnd" or "neg" or "pos"... the minus symbol, gnd, and neg all mean the same thing... that's ground/earth/return. The plus sign and pos both mean positive voltage. Many laptops have power supplies that output 18 volts DC... the "dot" in the center of the "C" represents the hole in the power supply plug or the pin in the center of the power supply socket on the laptop motherboard. Also, the laptop power supply MAY specify AC or DC output voltage. These are not interchangeable. If your power supply outputs AC power and the laptop is expecting DC voltage, the computer won't even begin to start. The label on the bottom of your laptop should have a small graphic of the power connection with the "C" and the dot in the center of the "C" just like the power supply socket. The voltage of the power supply output has to match the the input voltage indicated on the laptop label. If those are different numbers or different polarity, you may not be using the right power supply. If the power supply says the "neg" or "-" terminal is the outer (shiny silver metal) of the power supply plug, the laptop label must also indicate that the "outside" of the "C" is ground/negative. And the voltage of the power supply should match the voltage indicated on the laptop label.