Sita, I don't know for sure, but, as far as I am aware you cannot replace the board. I think it might be possible to replace the entire base camp, but I have never tried to do this.
Are you sure you actually have a problem? Or, could it be that there just aren't any adventures available at this time. The adventures are random and sometimes no adventure will appear for as much as a couple of days. However, there is always, to my knowledge an adventure available immediately you take your first sim in a new game to each of the three venues. In France you should immediately be asked to retrieve a mysterious object, in Egypt to obtain a relic from the little tomb just above the base camp and in China to find a relic in the temple like tomb near the market. After these three, the adventures are random and not always available immediately. You may just need to be patient. Try queuing up your adventure requests and if that does not work then leave it, and do something else, until the following day.
However, if you think there is a problem, then I would suggest doing a factory reset as this cleans the game and fixed an incredible number of issues. The factory reset is very quick and easy to do. See the stickies in "Technical Help" for instructions. If this does not help, let us know, I am sure someone else will have some ideas.
Good luck.