Sounds like you need a sump pump before you address the inside.

Hi, I've been researching rubblestone basements for the past couple of weeks since we've purchased a brick row house built in 1873. I've learned that you have to be very careful about sealing the stone walls. The stone and mortar are designed to dissipate moisture through them and if you waterproof the inside, they may crack and crumble with the freeze/thaw cycles or just because they remain moist. Further, it is said that only the same soft lime based mortars should ever be used in conjunction with them. I'd guess your concrete floor might be newer than the original house? Anyway, concrete is a different entity...much harder and shouldn't pose the same problems. I agree, though, with the previous poster that you don't stand much of a chance of preventing the dampness unless you can correct the problem first.