Unreadable data-CDs (10.3.9)



First time posting here, hope you'll be able to help me, since I don't know a lot about these things. I've tried the search-option and found related topics, though my problem seems a bit more selective, so a new topic. Hope that's ok.

Yesterday I got a G3 for free at work and I installed Panther on it (clean install, all previous data were deleted) and updated it to 10.3.9. At work I have an iMac (not the latest type, but the previous one) with the same operating system.

The problem now is that when I insert a data-CD with a .avi-file or a data-CD with strictly mp3's on it, I get the error message "You have inserted a disk containing no volumes that Mac OS X can read". The weird thing is though, that these very same data-CDs give no problem whatsoever on my iMac at work (that's where I made 'm for, to bring some mp3s to work). I also had another data-CDRW with a dmg-file on it and that one is read without any problem. Also audio CDs are read without problem and play fine.

What's going on? Can I fix this problem? Is it a software-problem? Everything else works perfectly, but I want to copy the contents of these CD-R's on this Mac. HELP!

Thanks in advance for any tips / advice!
It sounds like the cd drive could be on its last legs.
I have found that when a cd drive is nearing the end of its life first you get discs that it wont play when they should and it goes on from there.
then again it could be that you just need to clean the cd drive with a lens cleaning disc.