I'm sorry but based on your description I can only give you a very general advice. You probably need a professional (chimney sweep) to evaluate the chimney and determine what steps need to be taken for the chimney to function properly, and to remove that unpleasant odor.
If the chimney is sitting directly on the basement’s floor, it’s foundation might be completely deteriorated and allowing for ground water penetration. The same might apply to the lower portion of the chimney walls, its interior, and maybe other sections. If there was no cap on it for some extended period of time, no liner and crown to protect interior, there may not be easy way to fix it, it might require rebuilding.
Somebody needs to look at its exterior and interior to give you a full answer. It’s too dangerous not to check its structure.