Don't lose hope. I'm the one that filed the initial bug report. I was able to boot from a Live CD image on the hard drive using Grub 2 (http://ubuntuforums.org/showthread.php?t=1549847&highlight=boot+grub+iso) and the final pae flavor ISO saved to the hard drive. I have no idea why the pae version ISO boots from the hard drive using Grub, but doesn't boot from a USB stick. Anyone else like to explain that I'd be interested in knowing.
Today I tried a clean install using the mini.iso method (http://archive.ubuntu.com/ubuntu/dists/precise/main/installer-i386/current/images/netboot/non-pae/). Just downloaded and burned the mini.iso (non-pae flavor) to a CD, booted using the CD and clicked on "Install" from the menu. Just make sure you have the PC is connected to an internet connection so that the packages can be downloaded. There are quite a few questions to answer, but nothing that wasn't that straightforward. It took close to an hour by the time all the packages were downloaded and installed. But if you figure the time to download the CD image ISO, burn time to a disk, and install time from the disk, it's not that much different overall.
I ended up with a fully functional 12.04 generic non-pae install on my Thinkpad T42. So far, Precise working fine.