ASUS Eee PC POWER LIGHT TURNS ON BUT NOTHING HAPPENS SCREEN STAYS BLACK?

The RAM may be faulty or just needs reseating to make proper connection.
Reseat the RAM module/s and boot up the laptop.
If the laptop still does not boot up, remove the RAM module/s and take it to your friendly computer repair shop and get them to test the RAM module/s for you. If faulty, then replace them.

There are many instances for your hardware problem. These are the possible solutions: 1) Check and replace your RAM. 2) Check and replace your LCD inverter. 3) Check and replace your LCD itself.

If you see power lights but nothing appears on the screen, it could be a "POST" (Power-on Self Test) problem or simply LCD problem.

Here are some steps that you can try.

1. Remove the battery and the ac adapter then press the power button for at least 20 seconds to drain electric charges left from the system. (You may need to repeat this step to get it work.)

2. If above step doesn't work, try to plug in an external monitor and see if you get display from the external monitor. You may need to press the Fn + F10 or F6, depends on the key designed on the keyboard to toggle between displays.

3. If you get display from the external monitor, I'm sure your having problem with the LCD components. In this case, check and replace faulty LCD backlight, LCD cable or LCD inverter. The LCD inverter is often a culprit.

4. Try to reinsert the memory module/s (RAM) of the unit, try using one RAM at a time to see if it works. A faulty RAM will cause the issue not to POST.

5. If reinserting the RAM doesn't help, most likely your motherboard needs to be replaced.