Is this the first time you turned it on or, as it sounds, do you have a picture and sound then a black screen (after how long watching?) but audio continues?
If it has picture/sound then no picture, it sounds like your antenna/tv connection and setup is good -- the TV could be shot. If under warranty (and I guess it is as I believe the 30 series is new for 2011), I'd contact Panasonic via their web site and contact them with the particulars. I've used Panasonic support a couple of times and although not thrilled, they did get back to me.
I don't know what the return policy is for where you bought the TV but depending upon how long you've had it -- I'd give them a try also for return/replacement.