Problem 1 was that a dark patch had appeared in the lower center of the LCD on machine 1. You could still read the screen, but there was clearly something wrong.
Problem 2 was that the keyboard on machine 2 was wobbling. This is the machine we use to drive the Match Game SF sound effects, so yourbob might have noticed that the keyboard flexed when he pressed the YES and NO buttons.
This morning, the tech from Dell called saying that they'd sent him a replacement screen and he could come out and fix it. Shortly after 10 AM he arrived and set to work on swapping screens. After doing that, he offered to have a look at the other box to see if he could fix it. Also, he wanted to show me how to remove the keyboard so I could clean the cooling fan, as it had needed cleaning on machine 1.
To my immense relief, it turns out that there wasn't actually anything broken on the keyboard for machine 2 -- it just needed to be re-seated. So if Dell ever gets back to me on the second service request, I can cancel it. It's nice when the system produces good results like this.