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Am I going to have to add an IDE/SCSI PCI card? If so, do you have any recommendations? How would adding a card affect the existing SCSI chain?"
Your G3 natively supports IDE/ATA/ATAPI devices, having two ATA channels to do so. There is also an onboard SCSI-1 bus (max. 5 MB/sec), for connection of external/internal SCSI devices. Your profile info indicates the G3 Server, so you'd likely have an Ultra-SCSI PCI card and hard drive, if the hard drive is a SCSI device. The CD-ROM and Zip drives undoubtedly share one of the ATA channels. If that's the case, you still have an extra ATA channel for connection of extra IDE/ATAPI drives. What does the Apple System Profiler ("Devices and Volumes") indicate about the type(s) of installed drives? If your existing hard drive is connected to one of the ATA channels, you can configure dual drives as master/slave on that channel, provided that your G3 has a ROM revision $77D.45F1 or $77D.45F2
Assuming that you have the mini-tower model, the lone IDE hard drive in the top of the chassis usually has the single device OEM ribbon cable attached to it. If you want to connect a second drive as slave on the same ATA channel, you'll need a 24" (no longer) ribbon cable with connectors for both drives. The 24" cable has adequate separation between the drive connectors, enabling connection to each. Several years ago, I bought four of these ribbon cables (40-conductor, 24") from Radio Shack, but I don't even know if they still carry that item in their stores today. A PC store should have them. You can't use the newer 80-conductor Ultra-ATA ribbon cables, because they're typically only 18" long, and that's not long enough. Cables longer than 24" are prone to causing data corruption, so avoid them. For ease of connection, you may have to move the CD-ROM and Zip drives down one bay each, and install the slave hard drive in the bay formerly occupied by the CD-ROM drive.