I think it's safe to assume that Parallels emulates a different logic-board and chipset for Windows 98 than it does for Windows XP. This is why upgrading a Windows 98 VM to an XP VM and then changing the Parallels settings is not a good idea: it would be like unpluging your hard drive from one logic-board and connecting it to a different one and hoping it will work. You might get lucky, but don't count on it.
If it were me, and I had not already tried this, I would suspect that some files had been corrupted somewhere along the line and do the following:
1. Make sure I was up-to-date on all the Mac OS updates, possibly including a clean install of Mac OS X if I thought it might help.
2. After rebooting, make sure I was up-to-date on all the Parallels updates, again possibly completely uninstalling it, followed by a fresh install (rather than an upgrade), and then reboot.
3. If I had done a clean install of Mac OS 10.4.10, Parallels would be the first 3rd-party software I would install. That way I might be able to see if some other software introduced the problem I was having.
4. Manually build a new VM (rather than using Parallels automated process)
5. If all of these measures failed to fix the problem, I would then attempt to contact Parallels support and possibly submit a bug report through their proper channels, assuming of course that I haven't made any hardware modifications to my Mac.
From what you have described, it sounds like your VM cannot recognize/access your CD drive unless you first unmount it from Mac OS. If that is correct, it further leads me to suspect that there is file/driver corruption somewhere in your system. That's why a fresh /clean install of everything might be warranted.