Originally Posted by Loren Pechtel
That basically leaves the MB as the culprit--and even if you can get one it's unlikely to be economic on a machine that old.
I generally agree the MB or the CMOS may be the issue. You can check the hard drive condition by taking it out of the laptop and attaching it to one of those 2.5" drive USB cages/enclosures and then try to see its contents on a desktop or another laptop. Chances are you'll view the contents of the drive just fine.
It could be the power supply, but in my experience, a faulty PS doesn't even get the system to start.
You could also test if the display itself is faulty. I've had a couple LCD's go out and easiest way to confirm is to hook it up to an external monitor. You didn't specify if the LCD even shows anything at all, or has some basic logo/splash screen, so I'm presuming the screen itself is just dark.
Also, for memory issues, generally an error message will be displayed during the BIOS/POST if an error is detected.