Kyocera DA-310CX. It plays fine straight through, but when I try to
jump from track to track either forward or backward, it can't lock
onto the next track about 1/4 of the time. The track number is
displayed, but the countdown display stays blank (a series of dashes
across it) and no sound. It either does not play at all or every now
and then it will begin to play after a long delay with the track
number displayed, but the countdown does not start up. When it does
this, it begins to play from a spot inside the track, rather than from
the beginning. Now, if I jump forward, then back again, it does lock
in. It appears to play both CD-R and factory CDs in this way.

Is this most likely a cleaning/lubrication issue? Can I rule out any
problems with the laser or other unfixable problem? When you put a
disc in and play it straight through, it appears to work without any
problems, it goes from track to track smoothly (albeit it with a 4
second delay in between tracks, as designed).

The tray mechanism clearly needs cleaning, as you have to help it open
and closed or it does not move.

I have read the very good tutorial on CD player repair from this site
and will certainly look at the laser for cleanliness, clean and re-
lube.