Leaking basement caused by poorly graded sidewalk
you should be able to get the slab mudjacked (its a process where a series of holes are drilled in the slab on the low side, concrete is injected in under the slab and the hydraulic pressure lifts the slab up.  when the concrete sets, the slab is permanently lifted the way you want it to be.  just do a search for mudjacking in your area.