Strange. Ok, you hooked it up to the primary IDE AND you had the jumper set (on the CDROM) as Slave, correct? If you did this and it still didn't work, it would tend to sound like either the BIOS isn't recognizing it and you may need to go there and "Help" it out, OR the drive is bad. However, you tried different ones and they exhibited the same behavior so that doesn't make sense.
I think it is BIOS and/or OS related; not MB or drive. Let me ask, did you have or are you using an additional optical drive, such as a CDRW and/or a DVD? If not, I think you should place the jumper back to the Master Position on the CDROM, carefully hook the cables (ribbon, sound and power) to the drive and reboot the system. Go immediately into the BIOS and see if you can get the Secondary IDE to recognize the drive correctly. You may have to either select "Detect", or in some cases there is a separate option to list it as CDROM in the BIOS. After that, save and exit the BIOS and watch the boot process on the screen. Make sure the HDD and the CDROM are detected. This will happen pretty fast so you might want to have your finger on the "pause" button if you need to. Then hit any key to continue the boot. If all is well at this point then you are down to the OS. Go into Device Manager and see what is listed under CDROM Drives. Confirm that your CDROM is listed there and that no conflicts are showing. It's been a while since I've used 98 but I think you can also check that "autorun" is selected in the CDROM properties. Just confirm it is selected. If all is well here then you should be "good to go". Test it and see.
IF there is a problem detecting the drive in the BIOS, try one of the other drives you spoke of that you tested early on and see if they can be detected. If that also fails then change the cable and try again. If that fails then you are looking at either a BIOS problem or an IDE channel problem on the MB. However, since the Zip drive worked on IDE 2, I would think that this would not be the issue.
If it is detected correctly in the BIOS but not seen in Windows then it is an OS/driver problem. Win98 has universal CDROM device drivers though, so I'm thinking that would not be the issue either.
One test I just thought of that you could try is booting with your Win98 Boot Disk. When the appropriate screen comes up to start the system WITH or WITHOUT CDROM support, select WITH. The first set of dialogue will start the detection process and you should see it identify "1" device. If it says "no device detected" then there is a problem for sure. I'm thinking it will detect it though so let this process complete until you get to the A prompt. Then, see if you can access the CDROM drive. It should be either D or E, depending upon what other drives you have installed. At the A prompt just type in D: (or E🙂 and hit enter. Then, make sure there is a program or Windows CD in the drive. At the D (or E) prompt, type in DIR and hit enter. If you get a list of files that you know are on the CD, then you know the system can properly detect and use the CDROM. Pull the Boot disk and reboot. Test again.