A bit confusing what you write here. The "audio cable" that connects a CD-ROM to a sound card simply ensures that when you listen to audio CDs you can output the sound through the sound card instead of the headphone jack on the CD-ROM Drive itself. That audio cable should be a 4 pin cable. If you have that cable attached to the sound card or not doesn't matter unless you plan to use your PC as your Audio CD player. Most people won't even notice if that cable is missing.
Another cable is the IDE cable, your Hitachi CDR-8330 is a "modern" IDE CD-ROM with a standard IDE interface. You previously wrote that "The CD-ROM originally installed and attached to the sound card would just result in the computer giving a Hard Drive Controller error". I assume you had that CD-ROMs IDE cable attached to the standard IDE interface of your motherboard, the one the harddisk also uses. Good thinking, but some old CD-ROMs - even though the cable "looks" like a normal IDE cable used a proprietary interface, they came either with a seperate controller card OR could be attached to the sound card controller (Note that these are NOT attached by the small AUDIO cable, but by the IDE-alike looking cable). The sound cards usually came bundled with these CD-ROMs since there was no standard, so while CD-ROM "A" could be attached to the controller on Soundcard "X" CD-ROM "B" would require a different interface as on Soundcard "Y" and so on. Modern sound cards don't have a CD-ROM controller interface on them any more, but back in the days that was incredibly common.
If you look at the picture Gigabite posted of the AWE32 you can see 3 different connectors - in this case "Sony" "Mitsumi" and "panasonic" and that were just 3 interfaces of over a dozen that existed. So my guess is that the "old" CD-ROM in your computer might originally have been attached to the sound card and not the IDE.
If the "old" drive is actually a proper IDE CD-ROM and giving HDD errors on boot a common problem could also be the master/slave settings. Usually if that happens you have both drives as master, you can usually change that with jumpers on the back of the drive. Make the harddisk the master and CD-ROM the slave. As most motherboards come with 2 IDE interfaces another rather easy fix is to use each drive on a seperate IDE interface, not both on a "dual cable". That way it doesn't really matter if they are master or slave, tehy won't get in the way of each other.
To make it short - tldr:
- Your sound card gives errors on boot. It is not found by windows. The audio connectors is the wrong proprietary type. Sounds like it might be broken. Get some SoundBlaster clone for 2 dollars on ebay, install it and forget about the old soundcard.