I'm not fully working yet, but I think I have my problem figured out. I thought I'd share what I have found so far in case anyone else comes across the issue. (Or if somebody already has and wants to chime in with more info than I have figured out so far!)
I have a working Hacintosh that's been running well now for 4 or so years. It's a Dell E520 and yes, it is getting a little too old to keep using, and yes, I haven't upgraded the OS because I'd like to upgrade the hardware. But hey, it works, and Apple still hasn't come out with a midline desktop computer.
Today, after uninstalling some software, I rebooted. (I don't need to do that very often which is nice, so the last reboot was a few weeks ago.) Strangely, Mac Update started and said that it was updating my computer - I had seen it on the screen earlier today, but I had clicked "Not Now" and it had gone away. But I knew that the update was just a Security Update that had been bugging me for the last couple weeks so I let it go.
The computer wouldn't come back up. The BIOS ran fine and Chameleon gave me a "boot done" and then froze immediately on the "\" "|" "/" "-". Hitting power button to shut it off and then again to turn it on gave the same results. Eventually I discovered that disabling one of the 3 hard drives did the trick. Fortunately it is not the system disk. It is my Time Machine disk.
Apparently, Seagate drives have a known firmware bug that causes the drive to shutdown. In some cases, it fails to report to the BIOS at all ("BSY" error) and in other cases, it reports to the BIOS as a 0 byte size drive ("LBA" error). I believe I am seeing the latter and that Chameleon gets stuck when running through the disks and finding a drive that is zero bytes.
If the drive is under warranty, you can have Seagate fix it. If it isn't, like mine, you can try the fix yourself. And I may do that. But for now, I wanted to post that what appeared to me at first to be a Hacintosh-related error on a Mac update turned out to be complete coincidence and it was actually a hard drive firmware bug that confused Chameleon.