It is working now. The original cable is fine. I had to switch the jumpers from their factory defaults of CD as master and zip as Slave to the opposite.(CD-Slave, Zip-Master) It now recognizes both perfectly fine.
Also, for those who are curious, the drive is a Sony CD-R/RW Model # CRX140E.
Also, for those who are curious, the drive is a Sony CD-R/RW Model # CRX140E.