You may be a candidate for "mud-jacking" or "slab-jacking", depending on how you name it in your part of the country.
Either way you call it, it is a service that lifts slabs by injecting grout, or cement, underneath the slab thus lifting it hydraulically. they drill 3/4" holes into the slab fro above, attach a truck-mounted pump to a hose and then watch the whole slab rise to where you want it. Cost effective against new slab, but it is comparable to repours...a lot of factors go into it, but it wouldn't hurt to have a company quote on that to tell you those options may be.