|Problem with power supply, power button/cables for power button, or motherboard power button route. |
Try this first, can't hurt. Unplug system. Press power button a few times like 10 or so. Then plug in system and try again to power on.
If not then start at web pages that tell how to diag power button and power supply.
"Best Practices", Event viewer, host file, perfmon, antivirus, anti-spyware, Live CD's, backups, are in my top 10