If this happens after a few initial screens go by with no issue and then windows starts loading and it hangs then it's a software problem.
If the lines appear right away and you never see any software loading then it's a hardware issue.
It could be an issue with the video card, mainboard, LCD, or the wires that go from the mainboard up to the LCD screen. The odd part is that a video issue shouldn't stop it from booting, so that points more towards a mainboard issue.
Are you sure it's not booting? Maybe just the display is out.
Watch the disk drive light and see if it continues flickering for a few minutes after the video goes, out.
Did you have an trouble with the hinges on this laptop? Just asking because the display wires are tiny and fragile and they travel up to the LCD passing near the hinge area.
If you are brave and reasonably handy and can read a detailed service manual you could try reseating some of the internal connectors but that gets pretty involved and the problem is more likely with the LCD itself or the mainboard.
There is a lot of info about this on the Dell communities that covers many models and some of them mention known problems that Dell fixes for free. See the link below, then call Dell. Be polite but firm and mention the recall because it seems to cover the D810 so they may fix it for free.
http://en.community.dell.com/dell-blogs/direct2dell/b/direct2dell/archive/2007/06/19/more-systems-now-part-of-vertical-line-issue.aspx
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