The answer you recieved from Dave and Brian C were serious responses. There are potential problems with tiling over tiles. You do not know how well they are fixed to the wall, and depending on the tiles you wish to fix over the top, there is potential to pull the wall down with the extra weight you are adding to it.
It is quite quick to pull of the old board and reboord then tile. To tile over the top may save a small amount of time but it is also more difficult to get a good finish. Are the current tiles level for instance? You will also need to use a cement based (powder) adhesive and then you have the issue which was the point of your question, about the finish on the top.
Starting again really is the best solution.