Hi Steven...
If I understood correctly, the walls of the basement are now all dirt and the only concrete left is over the floor? In that case a dehumidifier will hardly handle the job, as the water is consistently seeping through the dirt and concrete. (Not to mention the cost of running a dehumidifier under these conditions)
And unless you live in a cold and dry climate year round, no amount of ventilation, at any given season, will ever dry the basement enough to keep it from developing moisture related problems (mold, rotten floor joists, termites, etc)
Depending on how big is your basement, I would suggest you consider treating it as we would a conventional dirt crawl space.
The sloping helps, but you might benefit from installing a drainage system and a sump pump. Then line the dirt walls with a thick and sturdy 20mil vapor barrier (about as sturdy as a pool liner) and depending on the size of the basement, line the concrete floor as well.This will keep the water that evaporates from the ground, out of your basement, while the drain tile collects the rain and spring waters and the sump pump discharges it as far as possible from the house.
You can then run a dehumidifier, to completely dry the basement and keep it dry.
When applied to crawl spaces, encapsulation can make the whole houst at least 18% more energy efficient.
I believe that you might be pleasantly surprised with the energy savings if you control the moisture in your basement as well, even running a dehumidifier.(Make sure you pick an Energy Star rated model)
Extra caution if you run combustion appliances (furnaces, water heater) in the basement; in that case you will need a professional basement or crawl space specialist to do the job. Those appliances need a consistent supply of fresh air to work and you can't risk depressurizing the basement with such appliances in it.