You don't get out of the jam. If there is truly no way of breaking through pawn chain, like by attacking the pawn chain with a pawn.... then you should maneuver your pieces behind the pawn chain into more productive positions in order to take advantage of any open diagonals or files.
Btw it's called a "closed position". You normally get a lot of moves to organize your pieces in a position like this.
Tied up games
If you have your game (usually I the middle game) tied up (like in a terrific traffic jam)- - -pawns in diagonals facing each other without the possibility of taking any, pieces with no place to go, etc.--- what do you recommend to get out of the jam?