|if it were me, i would cut the plastic piece off:|
first unplug the computer, cut the wires one at at time,
then strip each one back about 1/4 inch but leave them
apart. then plug computer back in, then touch the two bare parts of the wires and see if computer kicks on. if not, you have other issues and the repair shop probably necessary. If it kicks on, i would then proceed to radio shack or hdwe store and purchase a momentary-button-switch, power down and unplug, attach the wires (solder preferably, but if twist-up, be sure to use electrical tape on all exposed conductor), then mount switch somewhere accessible on front or side.