For the DVD if these are burn DVD they probably are the wrong Format for this Drive. Modern DVD Drives can use all Format DVD but some older ones couldn't read every DVD Format. So if you are using the wrong Format Blank DVD or even a Manufactured DVD it will be unable to read that individual Disc.
As for the CD as I read your question it is unable to read any CD's at all and this is probably due to the fact that the person who uses this drive has previously left Disc's namely CD Disc's in the drive a lot of the time and the LED that generates the Laser Beams has lost intensity and is unable to read CD's any longer. The DVD Readers/Recorders have 2 different Color Lasers that are generated by 2 Different LED's one for DVD and one for CD and these LED's have a [b]Limited Life.[/b] Once one of the LED's looses Intensity you need to replace the Drive.
Another Possibility is that the DVD LED has also lost some of it's intensity and is now border line so that when you insert a Recorded Disc with the wrong color Dye on it or any damage the Laser Beams are not intense enough to read the Disc.
The only solution if that is the case is to replace the drive with a new one.
The last possibility is that this is an old drive and the Dye Lots have been changed to something no longer supported by this drive. That means that a slightly different Color LED is required to generate the Laser Beams to read the Disc so again you need to replace the drive with a new one which is capable of reading all of the currently available Dyes.
Col