I think my laptop is fried

So i come home yesterday to hear my laptops fans running full tilt. I notice the screen (which should be off) was mostly black, except for random pixels here and there that were blue. I touch the track pad to wake it up (as if that would do anything) then to my horror i see what appears to be a fully corrupted image. Its hard to describe, but there were regular phantom blue squares spread out in a tilted grid pattern with garbled text behind. I quickly go to the virtual terminal and sign in through there and the screen is still garbled. I listed the running processes with top and saw that soffice.bin was running at 100% (libreoffice). Anyway I rebooted the computer a few times, but it seems the garbled screen is a permanent fixture. Do you guys care to venture some postmortem guesses as to what happened? Is the GPU memory fried? Are the interconnects toasted? What triggered this? While in the virtual terminal i got several kernel panic messages (thats what appeared like to me, though i had never seen that). I guess i cant complain about this laptop, it served me since 2006 faithfully. Although it tried to fry my ballz off a few times. RIP Dell XPS M1710. You are in a better place now.

Try to hook it up to a monitor to see if its the screen or the video card.

Take the battery out.
Unplug the computer.
Hold down the “Start” button on the computer for 15 seconds.
According to Dell, this discharges any static electricity built up in the computer over time.
This worked on my Dell 1501, it’s worth a try for yours.

Say what?! That makes absolutely no sense at all; static electricity doesn’t just “build up” over time (meaning months to years), nor have I ever heard of this happening. But then it is Dell…

Conversely, it sounds like there is a real problem with the GPU or its memory; once common problem is that solder joints break, due to the way they solder the parts on and repeated heating/cooling cycles. This is also a known problem, as mentioned in this article (do you know if your computer has a Nvidia GPU?):

(this is from 2008; they have since changed over to other solders, in part because lead is now banned, but they switched before that).