Three things to try. (the third one only if you scratched your monitor).
1) Turn off monitor, let it cool. Get a screen-safe cloth. Apply pressure over area. Turn on monitor (let it warm up, 30-60 sec), remove pressure. See if it helped. (This is for fixing stuck, not dead, pixels, but perhaps the liquid crystal has gotten displaced with a blow/scratch to the screen).
2) Check your connections. Both to the computer and to the power. Make sure everythings tight, and if you are using any extension cables or powerbars, try direct-connect. If you are using DVI, try VGA, or vice-versa. If you have one I would plug it into another computer as well. ALSO to double check it\'s a monitor problem, use the OSD (on screen display) on the monitor, and move it to be in front of the line. If it\'s affected, it\'s monitor, and not signal/hardware/interface. It\'s also a replace/return problem.
3) For a scratch on an LCD, use vaseline and rub it gently into the scratch, then wipe away the excess. Nothing really fixes a scratch, but this will make it less noticible.
Keep in mind that pretty much 99% of problems that can affect an LCD screen are not reparable by even knowledgable end users, so you might be SOoL. A quick google reveals that virtually every post on the net with \'vertical line\' problems on LCDs ends up in replacement/return. If you can\'t return/repair this monitor (too old), and the line really bugs you, then you might as well open it up and check for loose contacts or any obvious damage (hopefully yours isn\'t one of the ones all glued shut).