Water on Garage Floor - Damage Blocks

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I recently moved into a home with a water problem in the garage. The garage is heated by a furnace - when snow melts off the vehicles, the water pools in the front corner of the garage and does not dry. Over time, this water has soaked in to the block making up the exterior wall. It then freezes, which is busting up the block, causing it to slowly flake apart (at least this is my theory of why the block is deteriorating in an isolated area). There is a drain in the floor of the garage, but the water seems to go everywhere except towards the drain. I can squeegee the water to the drain, but this is a pain, and most of the corner is impossible to get to because of a large, heavy built-in cabinets. I have a two-part question. 1) What is the best way to address the damaged block? 2) How do I fix the floor, so that the water runs properly towards the drain? Thank you in advance.