Water coming through detached garage concrete floor
You need to remove the water before it gets to the garage floor level. Since you indicate that water in the backyard may be so high that you suspect water coming thorugh the sill plate (i.e. above slab floor level) nothing you do that does not address THAT will really work. 

So, standard approach (surround the garage with a drain, including a trench drain on the front to prevent rain from coming off the driveway into it, if it "slopes away from the driveway") will probably not be sufficient, if the water in the backyard is rising higher than the floor level. Drains only work if they have somewhere to take the water. 

As such, you may need to address drainage in the back yard, unless you want to get into something as expensive and extensive as raising the garage structure and pouring a new slab floor, at a higher level, with a different slope to it.