But then why would the noise be there also at home (therefore using the two rca connectors)? Mmmmmm....

Sorry, didn't catch that part. If both the home and car noise started at the exact same time, then it could be something wrong inside the player, like a loose wire or a blown component.

Then again, you can get ground loops in home equipment, too. When I plugged my player into a certain friend's stereo with the Sunpower brick, I got ground loop noise. When I switched to the compact plug-top adapter, the noise went away.