The line down the middle points to this being a problem with the screen's backlight. The backlight illuminates the screen from behind: the screen itself is essentially a coloured filter, which you wouldn't be able to see without a light source. From the excessive brightness I'd say it's possible the backlight has been receiving too much voltage from the rest of the system.
This could have been caused by a problem in the drivers for the screen. In normal use, they control the voltage to the backlight in order to make the screen brighter or dimmer, but it could be that in this case a bug made them supply too much voltage. The backlight is actually in two halves, which can be independently controlled (but usually aren't): the line down the middle appears if they're not quite receiving the same voltage.
If the problem went away on its own, there is probably nothing to worry about, but there is a small risk that the extra voltage may have permanently damaged the backlight. Normally I'd expect a voltage regulator to turn it off completely before getting to dangerous levels, but only the manufacturer would know for sure. As it's still in warranty, you should check with them. (They may also be interested to investigate this to avoid the problem happening again to anyone else.)
You say there's still a little whiteness around the edge of the screen when it's on but entirely black: this is normal for backlit LCD screens. It happens because the blackest black the screen can display doesn't quite manage to filter out all the light. The filtering is worst around the edge of the screen because that's where the light comes through at an angle (and on some displays because the light leaks around the outside of the screen). You probably just didn't notice it before because you weren't looking for it.
