more then likely the water underneath the slap had some part in causing the crack. There are some companies that specialise in repairing cracks, however getting rid of the water is the most important part of your solution. Hopefully there is some kind of aggregate or stone for drainage under the slab, if so a sump pump will go a long way toward helping. Simply trying to keep the water out by trying to fix the crack is an inappropiate way of handling the proplem the water must be taken away from the slab. Then contact a company that repairs cracks and you should be fine. Of course there are products that allow a home owner to fix a crack, if the water is out of the picture then this may be okay. Sump pumps aren't as outrageously expensive to put in as you think, however they may be inconvenient and located in a spot where you wouldn't want one.