no, dont wire it into the amp....because of the huge draw from the amp at times, it causes fluxuations of current in that wire, which you do not want your computer tied into. If you have an analog voltmeter (with the needle), check the voltage at the amp, you will see it move whenever the amp "hits"....
the perfered method is to run a somewhat heavy, FUSED wire from the battery to your inverter, see
http://www.mp3car.com/vbulletin/power-supplies/45155-inverter-wiring-question.html for my schematic on how to simply wire your inverter up.
personally, i would be alot more concerned about the extending of your screen wires, if you are hacking it form a laptop. make sure the power wires are seperated from the data wires (if you need more explanation let me know) and that the data wires are shielded at some point, this will keep your screen looking sharp with little interferance