On/Off switch unreliable Compaq Ivo N620c laptop

I purchased a used Compaq laptop. The only problem I have with it is that sometimes when I press the On button, it does not start. This is happening when the computer is completely off. Sometimes it will work for several cycles of turning the computer on and off without problems, but when it doesn't work, I have to try again and again and again until it works. I am on a low fixed income and can't afford a technician; I must try to fix it myself. When I went to the Compaq site, I found entries for Compaq Ivo N620c, but none with P4 1.8 M processors. Mine has the 1.8 M processor. I don't know if this has any consequence in choice of motherboard or parts, so I am trying to find someone who has experienced the same problem. When it works, there are three buttons at least two of which come on the minute the On Button is depressed. When the computer does not work, no lights come on until it actually works again. TIA for help, Steven