Never encountered the problem myself but I can speculate. The PS2 uses a single variable wavelength pickup system to read both optical formats. For some reason it may be that your system is having trouble changing the wavelength to read CD. It may be using the DVD wavelength to read CDs and getting disc errors.
In this case, a lens cleaner will do nothing to fix your problems. Call up SCEA tech support and demand repairs. If the charge is not to your liking, raise hell and they should surrender. Tech support is not terribly difficult to intimidate. Swapping at a store is an option for some, though I personally think it is stealing.