I signed lease for single family house, with effective date one month later, on date of occupancy, and paid security deposit up front. I almost immediately realized the house is damp and probably floods from rain in basement. I told landlord I wanted out of lease. She has not returned deposit. It's been over a month. Said she would charge me until someone else signs a lease.

Can she do this? How can I get a refund?

If you signed the lease, and paid the deposit, you are bound by the terms of that lease.

Read your copy, if there is any option for you to receive any refund, it will be explained in your lease.

Welcome to AMHD. I cited this in an earlier answer and will do so for you. You may not be able to terminate your lease without a little more effort, depending on the state you are in and the terms of your lease. Question: does your town or county have a health department? Is there a building code? Meanwhile, explore this: Property - Chapter 17

As you have figured out by now, you are bound by the lease, so what ever the lease says about breaking is what is allowed.

You may gain quite a bit of leverage if the property is in violation of local/state health codes and/or local/state lease requirements.