Model DP-J2070 I got it from a friend and yes there was a long period of non-use. I tried the unit and discovered the problem.
Thank you for the reply.
The issue you're having is due to the laser lens being either contaminated (dirty), or faulty (scratched or mis-aligned).
You can try several methods of cleaning the laser lens to see if it helps clear up the problem. The first (which you've already tried) is to purchase a CD/DVD laser lens cleaner disc, and run it through the system several times.
Next I would try purchasing a can of compressed air (available at Staples, Radio Shack or even Wal-Mart). Open the CD drawer, or remove the cover of the player by removing the screws on the sides and rear of the unit. Then spray the can approximately 10" from the lens to blow any dust off of it.
If it still doesn't work, you can opt to clean the lens eye itself, by using isopropyl alcohol, and a lint-free cloth to gently wipe the "eye". Then use a dry spot on the cloth to buff the eye clean. If the CD player is still not reading discs, then the lens or transport mechanism is faulty and would need to be replaced.
In this case you can use the link below to locate a Tech in your area, but keep in mind it may not be cost effective, or practical to repair this unit- as repairs of this type are often in the $150 range.