From Roxio's support site:
Due to changes made to Direct CD between version 2.X and version 3.X, discs formatted in the earlier versions can not be written to in the later versions.
However, they should still be readable.
What OS are you using? Direct CD writes CDs using the UDF 1.5 format, which XP and 2000 both read natively. You could try taking your CDs to a clean XP or 2000 system and see if you can read them there.
You could also try downloading Roxio's latest UDF reader, version 126.96.36.199, from the link at the bottom of this page. Since you already have Easy CD Creator 5 you shouldn't need to do this (it comes with Easy 5), but it might be worth a try.
Some other alternatives for rescuing your old CDs include ISO Buster and CD Roller. There are others as well, but this should get you started.
Once you do rescue your files, you might want to consider reburning them in standard ISO-9660 format for best compatibility and reliability, as Nemesys suggested.