Screen is black but fan is running
My screen is black when I turn on my laptop (fan is running). Tried pressing the power button for 20 seconds or more but it still doesn't work.
Remove the battery and trying powering it up on AC alone.
Hold a light up to the lcd, if you see letters then the LCD backlight (inverter) is probably out.
Remove the DVD drive and hard drive and power it up. I've seen bad hard drives that will stop a computer from reaching POST. (note to other techs: especially on HP all-in-one systems)
Once you try the above, and if nothing works, post back and we can see if we can drill it down a bit more.