Actually, it shouldn't be that much of an expense. First, you should check the house's original construction paperwork, which should be on record with the local city hall I would assume. Second, if that doesn't work do research on the time period of the house and see if they did a standard gravel/rock bed sediment prior to pouring the concrete. If they did, you most likely have years of moisture accumulated down there. Sub pumps aren't expensive at all and as long as you have a dedicated outlet, enough space for the ball bopper to activate it when water gets too high, you should be good.
Now here's the tricky part: installing the sub pump required you drilling into the floor, taking a chunk of it out to expose the space between the foundation and rock bed, and putting the pump down there. Not cool, I know, but its the easiest fix to the problem and can save you headaches from later on.
Get expert advice first and see if you can find a better way if you don't DIY it yourself. Hope this helps.