Lot of users in other forums suggest that it maybe because of fan malfunction, dead motherboard, monitor socket, graphics card, RAM being un-mounted or could be due to insufficient power. I do not believe this as everything was fine before installation of Avast 9. So it might be a software issue, my guess. So I disassembled the laptop and checked every parts.
Plus I removed the DVD ROM Drive and by removing it, I ruined it by accident. Unnoticeably, I cannot get it to where it was before prior to disassembling. There are 2 small parts plus 1 spring that I could not figure how it came out of it and where it should be attached. If someone knows how, please let me know.
After re-assembling the laptop (except for the dvd rom), I tried the Fn+F5 and for the first time the screen works for a few seconds and it went black again. It was like this for awhile. Once in every 2 seconds, the screen turned black. So I kept repeating Fn+F5 until I was greeted with Safe Mode, Start Normally and so on. I selected Safe Mode and for some reason it booted to Windows desktop but the screen turns on and off. So every time this happens, pressing Fn+F5 works somehow.
Next, I went to the Control Panel and removed Avast 9. Then I restarted the laptop. Would you believe that everything works fine after the removal of Avast 9? No screen blackness. Then, I installed Avast 8 and all is well. So my guess, Avast 9 is the culprit.
Olddog was right. It was indeed a software issue.
By the way, I did try the puppy linux and it didn’t work as I cannot go to BIOS and change the sequence of booting to DVD ROM Drive. So I had to go with the Safe Mode then.
Once again, thank you tech, zorgon, & olddog for all your help.