I have a Toshiba Qosmio laptop running Win 7. There is a setting that allows you to decide how long the screen stays fully lit, dimmed, how dim and when to turn off the backlight. When the backlight is turned off, you can still see that the screen is working if the room isn't too bright, so I think that is what you are asking about.
Go to "Start", "Control Panel", "Hardware and Sound", "Power Options". Select "Edit settings" and there will be 4 slider-type rheostats. They will allow you to set the timing and brightness as you want, or disable entirely.
(I also have an older model Toshiba Satellite laptop, much older than yours, Toshiba Satellite L-25 running Win XP. It had a similar functionality but it was easier to find it in Win XP!)
Of course, you might have a hardware or driver problem. If so, start by having a look at this answer, as it segues into hardware diagnosis after a similar suggestion as mine, about altering Windows power settings.