PS2 gives can't read disc message on new games only.

Which games are not working for example?

Are these original discs or burned copies? The PS2 has no firmware updates so all games are made the same way, however the PS2 can detect copies and will no run them.

You may just need to clean your disk. I had a problem like that before and it turns out that I just needed to clean the discs. They ended up working after that. Use just a little water and if that doesn't work put a thin coat of toothpaste on it and then clean it. It should end up working.