Thanks everyone for the advice and compliments. Based on your statements, I decided to take the risk and probe the display panel more aggressively. I learned a lot about how the panel is built and I thought I'd share my observations here for anyone who is interested.
First, I noticed that the two damaged vertical bars looked to be the same width, and furthermore the left one appeared to be two "bar widths" from the left edge of the screen, and the right one appeared to be one "bar width" left from the right edge. So I figured the panel was divided into sections and two sections were bad.
To test this, I measured from the left edge of the screen to the right edge of the leftmost bar and found it to be about 9.3 cm. Since it looked like the left edge of the bar was about two "bar widths" right of the left edge of the screen, I figured 9.3 cm should be 3 sections, and if I was right, the bar should then be about 3.1 cm, which it was. Ultimately I determined that the panel has 12 sections, two of which were damaged, and that these corresponded with the 6 driver chips I'll mention later.
Given that the damage was section-wise, I wondered if there could still be a problem with the connector. I wondered if some of the pins on the connector controlled different sections. So I cut away some of the plastic film on the back of the screen and started probing the board with my multimeter where the connector is soldered on.
I found that the rightmost two pins were ground and the next two were about 3.3 V, for power to the circuitry on the display panel. There were a few more, whose purpose I didn't figure out. But after that were clearly 7 sets of 4 pins each. Of each set of 4, the leftmost and rightmost ones were grounded, and the two in the middle had slightly different voltages, centered around 1.1 V. I realized that these must be differential signal pairs with the shielding being grounded on either side.
So, still wondering if these different pins might control different sections, and the damage was due to a bad connection, I did the next logical thing and started shorting stuff out with my screwdriver
I used a flat tip screwdriver to short the middle two pins of several of these sets of 4. I found that they controlled different aspects of the image. Some pins would make it lighter or darker when shorted, or cause other unusual color/contrast distortions. One pair would completely disrupt the display--perhaps a timing signal I figured. Anyway, the important observation was that messing with each set of pins affected the whole display. So the different pins of the connector did NOT correspond to different sections of the display, but rather to different aspects of the video signal.
The important conclusion here was that based on this I was sure the connections were OK and the graphics card was OK.
So next I decided to disassemble the panel completely. I took it entirely apart such that I had just the glass LCD layer by itself, which is rather translucent.
With a magnifying glass I could see clearly how the signals were organized to drive the pixels. Along the top of the panel there were 6 column driver chips. Into the center of one side of the chips enter signal lines from the PCB. All around the rest of the chip's perimeter are incredibly tiny wires which all curve around to the edge of the glass LCD layer. As soon as these wires enter the edge of the panel, they spread out at an extremely sharp angle in a triangular fashion to cover the width of the panel area for which that chip is responsible.
Interestingly, I noticed that one of these chips, specifically the one on the right, which was causing the colorful moving distortion, was quite hot, whereas the others were hardly warm. Also I could see very clearly that the two damaged vertical sections corresponded to half of two of the driver chips.
At this point it seemed clear that half of each of these two driver chips was not working. I wondered if there was a connection damaged in the flexible flat membrane that connects the PCB to the LCD itself which was failing to drive the input to those chips, which are evidently arranged in two sections each. However flexing the film around a lot made no change, so, along with the fact that one of the chips was very hot, I figured the chips themselves are bad.
I will have to do some research on how the chips are attached, because I'm curious. There are hundreds of tiny lines going into each of these long, thin chips, with no visible evidence as to how they are connected.
While I was there, I also observed how the row drivers are wired. Some traces run down the edge of the display and then turn and go into a chip on the film sticking out along the vertical edge of the display. A multitude of tiny wires run out from these chips, enter the edge of the panel, and fan out to cover the width of the area for which that chip is responsible, as with the column drivers. At the other end of the driver chip, more wires emerge and continue running down the edge of the display to the next row driver chip. It looks like the number of wires entering the row chip on the upper end and exiting on the lower end are about the same, so I am guessing it is a bus of some sort to which all the row chips attach.
Now, I'm sure there's some real engineer out there laughing about how much work I put into finding all this. But it was rather fun nonetheless.
Long story short: bad LCD.
Connector. Right two pings are ground. Next two are 3.3 V power. They go directly into a fuse (the part that says "TK"), labeled F1, 1.5 A, 63 V according to the silkscreen printing. Farther to the right, outside this photo, is a Maxim IC, an inductor, and various capacitors, so clearly this is a switching voltage regulator of some sort. I'm not sure of the purpose of the next 6 pins. After that however are the 7 sets of 4 pins each which appear to be differential pairs surrounded by shielding grounds.
Next are the strange driver chips, much unlike any other IC I've ever seen. How the hundreds of tiny wires in the surrounding film are connected to these chips is the most interesting part of the mystery I have not figured out yet.
Just for show, here is the LCD layer itself. It's translucent of course, and you can see my fingers behind it as I hold it up in the light.
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