A good part of the humidity in the basement and the resulting mustiness can be due to ground moisture diffusing through the concrete. The ground temperature is below the air dew point much of the year, resulting also in absorption of moisture onto the wall and slab surfaces. Uninsulated basement walls also can be a huge parasitic heat loss during heating season. If the walls have been insulated with framing and fiberglass batts, you might think about tearing that out and doing it right, using rigid foam board up against the walls, with sheetrock over that for thermal and ignition protection. First you would want to be sure leakage of ground water through cracks has been fixed. You also could seal the slab using something like Drylok; that also could be used on the walls before insulating. Some sound advice on insulating a basement can be found here:
https://www.greenbuildingadvisor.com...-basement-wall