Strange. One possibility is that the CD-ROM on both computers is not supported by the install program. If the CD-ROM is ATAPI compliant, then it should work. If it is a Soundblaster CD-ROM, it is not likely to be supported.
The way you describe it, it appears that your install program does not support the CD-ROM, but I would think it is unlikely that you would have this problem on two CD-ROMS unless they are the same name brand. I assume you are talking about "two diffferent CD-ROMS" as being CD-ROM drives.
I don't know if you are booting through the BIOS directly from the CD-ROM or not. If you are, read the documentation files on the CD-ROM (On another OS, like Windows). There should be files like README, or INSTALL. One of them should tell you how to make an install boot floppy. Make one and try installing it that way. Some distributions do not install directly from the CD-ROM. I'm not sure about Mandrake.
The only other possibility is that your CD-ROM disk is corrupt.