A line down the screen of my laptop?

It may be only a surface scratch.
In this case, gently rubbing it with some SOFT abrasive paste may do the trick. Try some tooth paste or Vim.

It may be an actual crack in the screen (often not straight or have a slight angle) or an electrical problem preventing the activation of a colon/row of pixels (strictly vertical or horizontal).
In this case, the only option is the replacement of the screen.

Electro
December 2013

I am afraid that the screen is broken. The only thing that will solve the problem is replacement.

T
December 2013