A sump pump usually requires a water collection system
(French drain) all around the basement perimeter under the floor. This will almost always cure wet basement problems.
Also, rain water must not pool up against the foundation. Do whatever you have to do (some suggestions are up above) to alleviate this.
Rain water and gutter water should not be run into underground pipes next to the foundation unless the water is unconditionally eventually carried some place else (forest? street?) some distance from the house with no chance of freezing up or filling up and then backing up.
A slab patio that collects water against the house is bad news. You would need to caulk where it meets the foundation and also dig a pit at the side to collect most of the water running off and put a sump pump in that pit.