We bought a house and a week after we moved in we got 6 in. of water in the basement. It was not discloused that this has occured several times before. What can of case do we have?

You can sue the seller and based on the fact presented you have a good chance of prevailing in a claim against them. Your cause of action would be for fraud, hat is the intentional misreprsentation or ommission of a material fact that was knowingly made with the intent to induce another to detrimentally rely upon it. Accordingly, in your case, you would not have purchased the house had you known of the leak in the basement (or you would have set aside money from the purchase price to remediate the problem). The monetary compensation you are seeking, that is your "damages", would be either what the house should have cost with the defect or your out of pocket loss. At this point, you should consult directly with a local attorney who specializes in real estate matters. After reviewing the details of your situation, they can best advise you further.

You may, based on what you write, have a relatively strong case for fraud: fraud is lying about--which in a real estate context can include failing to disclose--known material, or important, conditions or problems, which lies or nondisclosure where done to get you to buy. Since you have several people who were aware of the flooding, it is likely that you could prove in court the seller logically must have known, too--therefore, by failing to disclose, she very well may have committed fraud. If you sue her, you could potentially recover the cost to correct the situation, such as the cost to install French drains or the like.