It is quite common for older CD players not to be able to "see" home burned CDs because of the method of production. Commercial pressed disks have a very highly reflective surface so only a relatively low power laser is needed to read them. Burned disks have a much less reflective reading layer and the lower power of old lasers cannot cope with or "see" the low reflected light level.
For information, I have an old Technics Hi Fi system in which the CD player has died. I bought a cheapo Philips Expanium MP3 player (pocket sized) and plugged that in place of the 19" rack mounted CD player. On a purely subjective basis, the new player sounds infinitely better than the old system and is more versatile as well.
As far as I'm aware the track info for a CD is burned in the centre of a disk, and the info for a CD-r disk is burned on the outer edge. So older players look to the centre of the disk for the CD info and if it is not there then the disk cannot be read by systems that were made before CD-r's were common.