I would cut it out on the perimeter and lay fresh concrete. If you know how to finish it won't be a problem, if you don't then it can get pricey. The bottom line is the overlays are only as good as the base they are put on.
Napa has a special, if you buy $250 worth of brake related parts they give you a cabinet like that included. I think the cabinet is around $39 with the brake parts. Look into it, but if it was me I would pass on those.
I would disconnect the downspouts from the floor drain, that most likely caused the problem due to the main line not being able to handle all ths water at once. If you disconnect them make sure they are diverted far enough away from the structure so the water does not puddle around the garage...
One thing for sure is the crack in the middle of the slab will come back if you fill it, GUARANTEED. The only way to fix it is to repour the piece that is cracked.