Ok, so to test it, I re-connected the internal floppy drive to see if having it disconnected was the issue.  Its nonfunctioning (it just automatically ejects disks when one is inserted) so I still have to boot up from the external 800k drive.

Still will not give me the "It is now safe to turn off your macintosh" prompt and just restarts.  The 800k drive did *try* to eject the disk when it restarted, so the non-ejection issue could be a problem with the 800k drive.

I am still perplexed why this Mac, running System 2/Finder 4.1, just restarts automatically instead of shutting down...