So what is nomodeset, why do we need nomodeset on some computers and not others?
I don't know precisely what is causing the problem in this case, but can give my general understanding of the class of problems.
It comes down to different computers having different graphics cards (or the equivalent built onto the motherboard or into a laptop). They all can draw pretty pictures. However, except for really basic (read as slow) drawing, how the software needs to talk to the card is different for every card. In the Windows world, this means you need different graphics drivers for different cards. The issue here is that some new software/drivers for Linux which do something called "kernel mode setting" for graphics cards haven't been sufficiently tested/developed for the particular cards with which you are having problems. Specifying 'nomodeset' when the system boots basically tells the system to use an older set of software/drivers which does work (but may be slower or have some other issues that people would like to eliminate).
You might ask why not just make 'nomodeset' the default. Well the old software has problems/is slower. Worse yet, it may not even work on some newer cards. In this case the decision was made by the people actually writing this part of the software we are using to make the new method the default and allow an option to select the old one (and request bug reports). If we were booting from a hard drive, it would be easy to go in and make a trivial change on the machines with the problem and never have to worry about it again. Unfortunately, CDs are harder to modify.
If the machine has a floppy disk, the same small change can be made to my floppy boot helper as well for machines that require/can use it. If you are willing to have users select from a menu rather then boot without any input, both the CD and floppy helper can give the user the option of which mode to select. It should be possible to modify a USB stick to have a menu as well.
Actually, I believe there actually is a menu hidden in all of the current environments. If you hit a key (it may have to be escape) fast enough, you can actually get a menu and you can manually add the nomodeset option yourself every time you use that machine. It's probably easier to show you how to do this then to describe it.