Tony, you didn't state what type of interface your zip-drive uses, but I suspect it is a parallel port drive.
There are several drivers that come with linux that can work with parallel port zip-drives.
ppa, imm, and paride.
You can test this by connecting the zip-drive, loading a formatted disk.
After that use modprobe to load the different drivers. You can use dmesg as needed to check on what the drivers reported after loading.
Also check http://www.faqs.org/docs/Linux-mini/ZIP-Drive.html
which has a nice howto, although it is a little dated.