How to get rid of moisture in hardwood flooring?
Your problem is obvious. Moisture is migrating up from the slab.   I don't imagine anyone suggested to do a moisture check on the concrete before you started?  There are meters that can measure the % of moisture in concrete. With that said, it is never a good idea to put wood or laminate directly on concrete slabs or uncured concrete upper floors. In your case, you said the concrete was sealed. How was it sealed and with what? One of the only products that seals and creates a vapor barrier is DryLoc. Even using DryLoc, some sort of underlayment should be used. The old way was to lay pearlings across the slab, put on a plywood subfloor and then your finish floor.  Today there are several subfloor products that resemble 2'X 2" or 2" X 4" panels with a waffled plastic base and a resin embedded or synthetic subfloor attached. These panels interlock covering the concrete and create a vapor barrier. The materials in these products resist mold and mildew and allow any water to escape if you have floor drains etc. 

Unfortunately, once hardwood has cupped badly or water stained from the bottom up, it is usually junk and cannot be reused. Sometimes if the cupping is minor, exposing it to a very dry environment for some time will allow it to flatten out, but I sure would not count on it.  In your case, I fear you have no alternative but to rip it all out and start from scratch. This time, address the moisture or possible water leak in the concrete first. Use a proper subfloor, or select a different kind of flooring that is not susceptible to damage from moisture. There are several vinyl plank type floors that look like wood or tile that are good choices in a damper area.