Using Parallels on a Mac to run Windows may have an issue with regard to software having direct access to the CD drive.
Parallels may be using a generic driver that is exposed to Windows and then translating to it's hardware. It is unlikely to be able to give direct access to the hardware to a different OS on top of it without some sort of software shim.
I would reconsider this approach.
You could dual boot your Mac Book via Boot Camp (there are other methods as well but this works fine). This would allow you to boot to Windows directly on the hardware. This would definitely work. The downside is that you would need to to create a partition of your hard drive. Currently your parallels is a file on the Mac partition that has your Windows installed on it. You could make this file bigger via Parallels in order to give you space to work. This, however, is unlikely to be the only problem you will have with this.
You could get a Mac based ripping software. XLD is reported to work with Pure Read 3+. I have not tested it.