You'll want to first make sure that the internal hard drive is SCSI ID 0, with termination. If it is a different ID, your Mac may not boot form it by default, especially if your PRAM battery is dead.
To set it to ID 0, read the label on the hard drive. If it does not say how to change SCSI ID, use the brand and model number to look up the instructions on the internet.
I think that hooking up just a bare SCSI cable may cause a termination problem, either that or the SCSI cable is bad.
Like Bunsen said, make sure that all of your drives, internal and external, have different SCSI IDs. And also there should be a terminator at the end of your SCSI chain. (The Zip drive has a switch on the back to turn on its terminator.)