Another thought on draining condensate is to mount the dehumidifier high enough on the wall so as to drain to an existing place for it, such as the aforementioned washing machine drain pipe. A pump also would work, and you wouldn't worry about a pump not working during a power outage, because the dehumidifier wouldn't run either.
You might think about the source of the basement dampness. I'd expect that to be from foundation walls and slab, in contact with damp soil. There are products (eg. DRYLOK) that can be painted on the surface of concrete for waterproofing. If there is, from time to time, liquid water, indicating intrusion of water through cracks, address that first. The surface of the soil around the foundation should slope away, so surface runoff doesn't find its way to the footings as easily. There are plenty of sources of information on addressing water intrusion.
If it's just a matter of diffusion of water vapor through the concrete, which is considerably porous, then it might be prudent to cover exposed basement walls with rigid foam board (eg. type II EPS), covered with sheetrock for fire protection (a code issue). The sheetrock could be applied over 2x4s installed flat-wise, to create a space for wiring and shallow electrical boxes. If the "semi-finished" space is insulated with fiberglass batts installed between studs, tear that out and replace with rigid foam boards and sheetrock. Fiberglass batts have no business being placed against a concrete basement wall. Yeah, I know, plenty of basements are insulated that way, but it's flat out wrong, counter to sound building science. Once you've insulated the basement walls the right way, you've retarded the inflow of ground moisture to a huge extent, reducing the load on a dehumifier and making the basement more comfortable and less musty smelling.
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