You said:
The CD drive isn't old...The CD drive is 16X
"Not old" generally means 3 years or less. Unfortunately, your drive probably doesn't have the ability to read CDRW's. In a couple systems that I maintain there are 2 CDROM drives (16X and 24X ). The 16X cannot read CDRW's but the 24X can. I'm not sure where the cut-off is exactly, but it all depends on the quality of the laser each one has.
Are you testing a data CDRW or music CDRW? Regardless, you must make sure you aren't leaving any sessions open. That way the table of contents is written. If that doesn't work and you must have compatibility, CDROM drives are cheap nowadays. Consider upgrading...