|"Problems with the built in LCD displays are common."|
That's one of the most frequent problems we get people posting topics about on this site regarding laptops and netbooks. If you scroll down the lists of topics you'll see that.
"I tried taking out battery and connected directly with the adapter, the white line blinking still comes."
Problems caused by the battery or the AC adapter or the power circuits inside the laptop probably cannot cause your symptoms, and especially since you say the display is fine with an external monitor.
See the info at the link in response 1.
Your problem probably cannot be caused by a failing backlight (CCFL) - it might be caused by a defective voltage inverter, or by damaged wiriing between the video adapter and the display especially if you have opened and closed the case a lot, but I think it's most likely it was caused by physical damage to the display assembly, whether you were aware it had been subjected to that or not. Laptops / netbooks are vulnerable to damage done by anyone whio has accesss to it, with or without your permission or knowledge, and only you know whether others who you know can access the laptop would be likely to tell you if they did damage it - some people won't tell you unless you ask them, or won't tell you in any case unless they get caught doing it.
"May be I made wrong choice in buying this compaq. I could have gone for others."
It's a universal problem - it's not specfic to any one brand. In any case, if someone damaged it, the brand's reliability has nothing to do with your problem.
Although, there is one brand that has a reputation for standing up better and being able to put up with more physical trauma - Panasonic's Toughbooks - but they cost more for a model with the same or similar specs.
Sooner or later laptops will come with LED LCD displays - there are already TVs and external monitors that have that. They use LEDs instead of backlights (CCFLs) behind the LCD grid as a white light source and need no voltage inverter. LEDs last a lot longer in theory than backlights (CCFLS).
Have you ever seen an actual led burn out on anything on or for a computer, or on anything else that supplies an accurate voltage to the led ? I haven't.