If all you get is the power light, no fan, no drive sounds, system had hardware issues. Try to run it without the battery. If that does not help, reset the BIOS (will need to take out the BIOS battery for a few seconds inside the case).
Have you tried an external monitor just to rule out a bad screen?
Next step is to try new RAM. If that did not help, you are looking at a system board replacement. If the laptop is old probably not worth the labor and part costs.