Can you give me a picture like the third one on the opposite side, the side with the DC+IN written. You remove the rest of the DC jack, that is good for connecting the wires. Measure the voltage from the adapter not soldered to the motherboard, you put the multimeter on a scale of 20 volts DC, if you don't have this scale put to an higher scale. Measure the voltage for the adapter connected to an outlet (110V), you put the red probe to the center wire and the black to the other wire, you should read around +19.5 volts DC. (Sorry if this to much informations, I don't know your skill level).
If i wire it the other way, would it fry it or anything? I have the positive to where there was a + but what if that is wrong? What would happen if i solder it the other way? Seems i got ripped off on kijiji and this is fried anyways. Nothing to lose at this point.