Not the case here. I can’t read any CD – data, audio, bought, burned, borrowed or blue.
DVDs – both movies and self-burned DVD-Rs – open just fine.

What filesystem do data DVD-Rs use? Do they also use the ISO-9660/Joliet file system like CDs do? Maybe they don’t and that’s my problem?

Did you try a LiveCD?

Try Knoppix or some other LiveCD with good HW detection (maybe a Windows install CD?). See if the problem is with your machine or with the OS.