I had the same problem with my 160 GB. I was going back to work and it was playing just fine, stopped at a store and then continued on my way and it would not play. It was recognized and the song title was recognized on the radio but there was no sound coming out of the speakers. When I got to work I played it in my office and it was fine in the Bose dock that I use. I tried to use a different cord and nothing, same problem. I had to take my 120 GB Classic and use that for my car. I have a 2014 Subaru Crosstrek.
I do not know why or how it won't play in my car via USB but it does work with an AUX cord. Try that and you should be ok unless you have another iPod to use instead. I have been searching for a reason why my 160GB just stopped working in my car and this was about a year ago that this happened.