Clean the lens with isopropyl alcohol on a cotton swab and then use hot water(Very lightly) on an other swab to remove the traces. Lightly use a kleenex to remove the water.
If it doesn't work, the laser pickup might need to be changed. There are a lot of popular models, but if this one isn't, a new CDP is needed. A $30 DVD player could play MP3s.
Also, there's a small adjustment control on the pickup itself. If there's one, it's the laser power normally. With a small screwdriver, the power can be raised a bit and it might work again, but I can't say that it will be a long term solution since the laser is being burnt faster that way.