Other users have connected successfully the spectrum analyzer to the line out of their car cd players. I don't know why you are getting that strange behavior. First you should check that signal is really coming out on that line_out port maybe you need to activate it somehow and once you are sure signal is coming from the line-out you should check the connection (cables,connectors,etc.) up to the spectrum analyzer. If everything is okay up to this point I see no reason for it not working.
The spectrum analyzer is designed to be plug and play with a standard mp3 player output which is pretty much standard across different players. It was not designed to be plug and play with car audio players but as most car cd players have a line out connection which goes up to 2V it is possible to connect it to a spectrum analyzer as that is within the limits of the spectrum analyzer. The onboard pot also helps adjusting that input level to get just the right amount of level showing on the analyzer.
There is also the option of having it installed by someone with experience in car audio setups.

