The CDs that the computer won't read: Are they factory-made CDs, or are they CD-Rs that someone made?
Ther are two very, very common problems why a PC can't read a CD-R:
1. The CD-R is on a crappy brand of blank CD. There is a BIG difference between different brands of blanks! For example, it's been my experience that memorex blank CDs are garbage--the worst of the worst. I have many computers and many audio CD players that simply will not read any Memorex CD-R, period.
2. The CD-R was made with what is called "packet writing" software, like DirectCD. Packet writing software lets you record on a CD just like it was a floppy. No special burning software, you just drag files onto the CD icon.
Trouble is, not very many people know that a CD you make this way is *not* a standard CD. A computer that does not have packet-writing software installed on it can not read a CD that is written this way unless the person who wrote it does a special extra step called "finalizing" the CD.
If I have this software, and I drag some files onto a CD and hand you the CD, you won't be able to read it. In order for you to read it, I must "finalize" it. Finalizing it means that no more files can be put on it, even if there is still plenty of space left.
There are also other possibilities, but they are less likely. If the CD is a Mac (HFS or HFS+) CD, a PC can't read it. If the CD was made with the standard built-in Mac burning software and the computer is running Windows 2000 SP2 or later, the PC can't read it--Micrfosoft deliberately crippled the ability of PCs to read certain types of Mac/PC hybrid discs, in an effort to make it harder to move information from Macs to PCs.
If the CD is a factory-made CD, then the problem is likely that either it isn't a PC CD or the laser lens in the CD-ROM drive is dirty.