Computer will not turn on

Of course you have verified the problem is neither the outlet, cord nor connection at the machine (I've seen people who "thought" they had plugged things in find out that they really hadn't) - if you're comfortable opening up the machine. Use the correct guide to access the Diagnostic LEDs If no light comes on, and you have not perviously accessed the cable from the power button, you could check for voltage at the power supply (if you have the proper tools and know how).

Remember to return and mark accepted the answer that best solves your problem.