I would angle grind or dig that out, and get it nice and level. Once relaid with new concrete I would seal it with PVA or some nice epoxy garage floor paint once its dried after a few months, as quite often you can see through those floor tiles and this will look smarter and stop dust coming through.
Once that is done I would go for a floor tile or even carpet tiles, I used carpet tiles in my current garage and they are very nice and comfy - easy to clean as well. I have 4 extra tiles that I place where the wheels sit to avoid too much wear.
I then replaced my garage door with one of these:
http://www.sws.co.uk/products/seceuroglide/roller-garage-doors they seal beautifully and work very well.
After all of that you will need a dessicant dehumidifier, ecoair are pretty good. Try
http://www.dry-it-out.com/dehumidifiers/car-storage and
http://www.dry-it-out.com/car-storage-faq for information.
Have fun, the results are pretty rewarding!
