I would repot it with fresh soil (knock off all the old soil, rinse away the roots so you can see root health) and remove the dead stems after you determine what is okay and what isn't. A clay pot might help keep it from being too wet in the short term (your call). I would probably put it in a smaller pot either way you go until it gets some healthy growing stems going again - at least to late spring/early summer. Make sure you put it in as much light as possible - next to a sunny window or under some artificial light for 10 to 12 hours a day.