Your cactus may be suffering from root rot, which causes the symptoms that you are seeing. Rot is usually from overwatering or not giving the soil enough time to dry out between waterings. To see if the roots are in trouble gently remove the plant from the pot and brush away the soil. If the roots are mushy you can try saving the plant by cutting away the soft areas with a sharp knife. Place the plant in a dry area for a few days to a week to allow the cut area to callous over. Once dry, replant it. You can also try cutting the top, healthy areas off the plant, and if they show no sign of browning where you cut them, set them in a dry spot out of direct sunlight for a month or so. When the base has calloused over you can try replanting. Be sure to use a cactus soil mix, which is designed to retain some moisture but not as much as a regular humus-rich potting soil. Here is some additional information on growing cacti that you might find interesting.

http://libguides.nybg.org/cactiindoors

https://extension.arizona.edu/sites/extension.arizona.edu/files/pubs/az1399.pdf

http://pss.uvm.edu/ppp/articles/cacti.html

http://ccenassau.org/resources/cacti-and-other-succulents

Hope this helps.