I don't want to come across a fear monger but I felt I should let you know about the zd8000's because the problem is very similar if not the same.
I have an HP Pavilion zd8000 and there has been numerous reports of the white line (actually it can be numerous vertical lines of any colour) appears, then down the track another vertical line appears until there are a few of them. I believe there was some sort of class action happening because of it.
It turns out with the zd8000's that it is actually a monitor problem and because most of the machines were out of warranty HP wouldn't do anything about it. The ones that were under warranty had the screens replaced but the problem recurred later and often after warranty.
I thought I should let you know because it is definitely something you should contact hp about.
Below I've linked a site that was developed specifically for this problem, if you notice at the bottom of the web page there is a link in regards to "Vertical Line dv6000". I realise it is a different model but there must be a link.