I see your problem: Water freely flows to your sill. We had a similar problem with a slab under steps that actually tilted toward our home and channeled water toward our basement wall. I removed the slab and landscaped so I had a very good grade away from the house. I think you need to do the same - hire someone to cut that slab fairly close to your house, remove the outside part, and then landscape so you have good water drainage away. If you have overhangs or eaves above, this could then keep much of the water away from your sill. Add gutters if you do not already have them and extend your downspouts a good 4-8 ft away from your house.
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