What happens if, after battle, board is still full?
You have another Battle immediately.

On page 5 of the game rules:


  If at any time during the game the board is filled up and no single space is left to place a tile on, a Battle commences (see BATTLES section below).


Even if the Battle results in a stalemate, the game will eventually end. As soon as the Battle ends, so does the active player's turn:


  The player who starts a Battle (by playing Battle tile or filling up the board) finishes his turn, regardless of the number of tiles he has left. As soon as the Battle commences, no other tiles can be used or even discarded.


As such, the next player takes their turn, drawing and discarding. Because the board is full, a battle happens immediately (before they can play tiles or use other abilities). Eventually, a player will draw their last tile. An automatic battle happens on that turn due to the board being full, then again on the opponent's turn, and then the final battle happens.

If both HQs have the same points left, each player takes an extra turn (a.k.a. two more battles), and then there's an additional final battle. If there's still no winner, it's a draw.