Hi Pooky
Does this happen every time you boot or when you resume from hibernation ?
Booting into safe mode... is this line still visible ?
You say it is black, but you can see the contents underneath the blackness... is this there when it POSTS at 1st power on ? If you go into the BIOS, is this line still there?
If it is there in the BIOS, then it sounds like a loose connection.
If only in Windows, then it may be driver related.... Windows update with Win 7 used to try and update my graphics driver from time to time, and completely do the strangest things... I had to disable automatic updates to stop this, and re-install the last XP driver from the HP site for it.