the coil in the inverters go bad and then causing the lcd bulb not to turn on. you can either change the coil or get a new VDU (inverter for you new-schoolers )
the pins can be fine but it doesn't mean the socket it plugs into isn't damaged. i've seen tons of pcmcia slots where the socket is damaed from people probably pushing the card in too deep. the socket needs to be replaced if that is...
if you have a voltage meter then you can quickly see if it is the AC adapter. if you do not have one then you can probably go to any compusa or whatever and have them test it for you. the test literally takes 2 seconds
could be the headphone jack has cold solder but without actually seeing it, its only a guess. the jack itself could be physically damaged and need replacing
if its the actual DC connector (not the AC adapter/AC cord) then it can be fixxed easily. ive seen a lot of the gateway DC's physically break pretty bad and need a new DC. if it needs a new DC or need to repair the DC, then i can help...