Easy solution. Replace the window sill. Carefuly pull off the side casing and any other moldings that are holding in the sill. Pry off the sill and cut a new one from matching stock, then reinstall and finish. If you do not have tools to do this, you will need to contract for the job. If you can remove the damaged sill and have a carpenter fabricate the new one, it will save quite a bit of money and time.
Thanks for describing the damage a bit better. I don't know if your sill is finished natural or painted. If it is painted, a wood filler, sanding and refinishing is going to be an easy repair. If the sill is stained and finished, the repair may show, but its worth trying to fill and sand. My original assumption was that the sill was damaged beyond repair.