Recently my laptop has been behaving very peculiarly. After it has rested for some time (10 minute plus) and I try to turn the computer on, 4 of the 5 LEDs on the face of the keyboard light up. The 5 LEDs are 1. hard drive 2. mail 3. num lock 4. scroll lock 5. caps lock. Everything lights up except the mail LED. As this happens, the laptop screen is totally blank (black). If I try to turn the comptuer off by holding the power button 5 seconds, nothing would happen; the lights and power remain ON and screen remains BLACK. The only way to turn it off is by unplugging the power cord and removing the battery, which is what I do. However, after I cut off power from the laptop completely (unplug cord and remove battery), if I replug the cord and hit the power button, the laptop would boot up normally like before. The computer would remain just as normal as long as it stays powered on.
So, right now, to turn on my computer, I basically have to hit power button, cut power source, and hit power button again.

Can anyone help me?? I would really much appreciate it.