Sony Vaio black screen

[NCHornet]

Having a major problem with my wife's laptop. It is the model PCG-7154L . If I have the computer plugged into the wall the green light is on for the Power icon on the front edge of the computer. Strange thing is, the battery icon is also lit solid. On my Vaio If I turn the computer on with it plugged into the way I get the same green light showing it is receiving 110 volt power, but I have no battery light that is on unless I unplug it. I also have a small light on the front of my computer that is blinking real fast, I suppose this simply means it is working. On my wifes computer I have no light. There is a icon and a symbol, but the light isn't blinking. The screen is just plain black. No picture of anything. She only uses this laptop to cruise the internet a few hours each week. We have had it less than two years, so if anyone could give me a hand I sure would appreciate it.
Thanks
NCH