Solved, or at least Closed
I started from scratch by reformatting and repartioning the disk while it was connected to an IDE cable instead of a USB external drive. Installed Linux Puppy 5.1.1 from the LiveCD to an ext3 partition and allowed the installation to put grub in the MBR. Then loaded FreeDOS to a FAT16 partition. Now I get the grub menu at boot and can choose either OS. I think my problem was in some boot-related configuration file that I don't understand, but will perhaps discover now that I have a functioning installation.