Blue Vertical Line
It is sounding like when the laptop is turned on and heats up a bit, the line appears? Sounds like one of the panels is going bad or atleast has developed a problem.
below are some tricks you can try to lessen the annoyance of the line.
Dual-Scan STN displays are composed of 2 panels behind a single protective
panel or screen. Because you are looking through the protective screen the
display appears to be one large panel even though it is not. There is
a physical separation line (gap) at the point where the two panels meet.
When the computer is on and being viewed it is not unusual to see the
visible separation line with the Dual-Scan STN displays. The line, actually
the fine gap between the display panels, appears because the color and light
pixels cannot run along the very outside edges of the panels. This line
(gap) between the panels can be seen as a fine gray line and is most
noticeable when viewing on a screen with a white or light background.
Note the line may not be as noticeable when the screen is displaying certain
colors or darker backgrounds.
It is not possible to completely eliminate the line but there are some
things you can try to reduce it's visibility.
1) Lower the display brightness/contrast. The brighter the backlight the
more noticeable the line.
2) Use Wallpapers and Screen savers that use darker colors.
3) In the Control Panel/Display applet under appearance try different
combinations of color schemes for your Window and Background choice
Let me know what happens.