I will try to help you with this question!
Is this line staying on the same place,doesn't matter the picture content,or picture aspect(wide,or 4:3)
Is this line a thin line,appears to be ove the whole picture,including the menu display?
When was the tv purchased(this is a 2008 model)?
I was hopping the tv is still under manufacturer warranty,because there are only three possible causes for this issue,and I was thinking you might get this unit repaired under manufacturer warranty.
Let's start with the first one;
-a poor connection on the ribbon cable connecting the C board(corresponding the black bar) to the plasma panel.This is pretty easy to check,just look at this connector and compare the connector position and lock with the others next to it.
Open unit up ,and look along the bottom,you will see these brownish ribbon cables,going from the plasma panel into the C boards-the horizontal,narrow boards along the bottom.Check these cables/connectors.
-another cause would be the corresponding C board itself.
-The last cause ,and this is the one I'm afraid is causing the problem on your set,is a blown TCP circuit.This is a circuit inside of that brownish ribbon cable,corresponding the black bar position.
If you disconnect the ribbon cable-unscrew the heatsink screws,and unlock the connector from the C board-you will see a circuit inside that cable,covered with some gray resin.A change in color on this resin and a pinhole burn,indicates a blown TCP ic.
Now unfortunately,this is something will require the plasma panel to be replaced ,since this IC/ribbon cable is a part of the plasma panel-not replaceable by itself.You can actually disconnect 2 ribbon cables,the one where the bar is and the next one,then compare the TCP circuits inside of the cables-this way you can see the blown one easier.
To replace the plasma panel outside of manufacturer warranty will be not economical,the price of this panel will way exceed the cost of the tv.
My suggestion to you is to call Panasonic and,since the warranty expired not to long ago,to try and see if they would extend your warranty,and cover this repair.
Sometimes they do this kind of concessions.
I hope this helps you at least get a glimpse about what is going on.Sorry for the bad news,but being a professional,I have to give you the right information,even though it might not be what you expected.
Thank you and have a great day!