It can be done but its going to be a bit of reverse engineering. Usually the base is cut to shape and the edges are glued to the base. I am assuming you still have the edges attached to the board, you will need to cut the sheet so that it fits inside the edges as best you can. Scrape off any high points in the old resin, mix up a batch of resin and put your new base material in, hopefully it has been flame treated or it wont stick. Vacuum bagging is going to be your best bet as setting up a press isnt exactly cheap. Once the resin has cured remove it from the vaccuum bag scrape off all the excess resin that has squeezed out, take it to a shop for a base grind, wax it and you are done.
It makes buying a new board look pretty attractive doesn't it.