You are correct madam. Continued exposure to moisture and water will eventually rot the wood in the wall and the wallboard. The fix we suggest may do the trick, however it should be noted that replacement of the portion of the floor that slopes improperly is the correct solution.
First, trim the wallboard an inch or so away from the floor so that it cannot get wet from the puddling. Next, drill quarter-inch holes every few inches between the floor and the mudsill (the horizontal bottom piece of wood at the bottom of the wall) so that water can drain through it. Spray inside the holes with Copper Green or some other product that contains copper napthanate ? a pesticide and wood preservative.
It might also be a good idea to add ventilation to your garage. Air can help to evaporate the moisture in the summer. If the holes don't clog with dirt or ice you should be OK. Also, don't drill the holes if the outside perimeter is not somewhat lower than the inside.