I'm assuming that this is not hardware... the optical drive
will play CDs with VLC, but won't mount data CDs
The disk is data CD burned with K3B on my laptop (Debian 7.8.0),
but won't automount, nor manually mount. As quoted above
NTFS has nothing to do with the disk as fas I know,

Try:

Still no-go, works on laptop, not on desktop

looks like your desktop is missing iso9660 kernel module. Try
lsmod |grep iso9660

There are also optical type problems which explain your symptoms. Does it read a pressed cd (as opposed to a cdr?). There are three very fine adjustments that control reading. In the hardware, they are set using special equipment by potentiometers and sealed with wax, or thick paint. Values drift over time, and the thing slowly alters it's reading. Not reading CDRs(especially lousy quality CDRs) is the first sign of optical degradation.

three things.
Degradation is unlikely - the PC is only 6 months old.

lsmod|grep iso9660 - shows blank
How do I install it?

plays pressed CDs, burned DVDs.
Does not play burned CDs or DVDs, and won't read burned
data CDs and DVDs

cheers

PS I use TDK blanks.

Try:

Also check that your user is in the cdrom group.

I assume you mean:
Plays pressed CDs and DVDs
Does not play burned CDs or DVDs. (I assume music and movies.)
Will not read burned data CDs and DVDs

I assume that all burned discs will work on the laptop.

Did you burn all the discs on your laptop?
Have you tried playing or reading them in other computers?

Post the output of the command (as root):
modinfo iso9660

Hello,
modprobe iso6990 shows nothing.
Yes I am the cdrom.

Is your desktop considerably older than your laptop, if so it may be track alignment incompatibilities, or it will not read CDRW/DVDRW discs.

That's normal modprobe iso9660 might do something. It shows nothing. Check with the command I gave earlier.
lsmod |grep iso9660

lsmod|grep iso9660 shows blank (already posted).
The desktop mchine is 6 months old, the lap 6 years.

Can you answer my questions from my earlier post?

michaelk...

I assume you mean:
Plays pressed CDs and DVDs --->Correct
Does not play burned CDs or DVDs. (I assume music and movies.) --->Correct
Will not read burned data CDs and DVDs --->Correct

I assume that all burned discs will work on the laptop. ---> all seem to work, but
it is difficult to tell which were burnt under Debian 7.8.0, however backup DVDs
for 12 Jan, 19 Jan, 26 Jan, and 2 Feb 2015 (all created on the desktop m/c) do
mount on the lap. This proves that the optcal drive on the desktop m/c was working
until a month ago.

Did you burn all the discs on your laptop? ---> NO, backup DVDs are made on the
main desktop system. I found One data CD created on the laptop: it works on the
laptop, but not on the desktop pc.

Have you tried playing or reading them in other computers? ---> I don't have access to
other machines, but i could if pushed, but I think that the laptop proves that the
fault is with the desktop pc (both running the same Debian 7.8.0).

Post the output of the command (as root):
modinfo iso9660

Do you have wodim installed?

Try burning a data cd with one of the options -tao, -dao, -sao or -raw96r.

Check which works in desktop.

I think it is a problem of compatibilty. Also write in lowest speed supported e.g. 2x