I am going to assume that the ZIP and CD burner are IDE devices. And that you have a regular CD and Hard drive.
Try this configuration.
Put the Hard drive on the 1st IDE cable as a master drive. Jumper the Burner CD as a slave drive and put iton the same cable.
Put the ZIP drive in as a master drive and put it on the 2nd IDE controller. Last jumper the normal CD to slave and attach it with the same cable as the zip drive.
Try that and see if it works.
If the system still does not boot! Disconnect the CD burner and leave the Hard drive by itself and see it it boots.
If it still does not boot, remove the Zip drive.
Now if it does boot, reconnect the CD Burner.
IF it does boot then the Zip drive interface it bad! Replace the zip drive.