This happened to my PS2. I don’t think the program is working to play DVDs on it.
There are ways to go in and clean it- we personaly don’t recommend taking the top off and going in unless you are sure of what you are doing.
I have seen some people suggest using a small bit of rubbing alcohol on a q-tip to clean the lens. I’m not so sure of this being a good idea in case some gets into other circuitry and completely ruins the system. There are cleaning kits available at game shops- next time you are in maybe the staff there can suggest something.
One other possibility is the lens may have been slightly misaligned inside. Again, fixing this will require going inside the PS2. Instructions on this can be found through a quick search also. i would try the cleaning kit solution first.
( here’s a link to a forum post: http://www.absolute-playstation.com/playstation-network/expert-playstation-2-hardware-accessory-help-playstation2-ps2-console/16660-i-cant-play-dvds-my-playstation-2-a.html )