Hi Chevy Bel Air
To say the same thing that Puzzled said, you could say this:
Some people never stop talking. They
also do not listen to what you say, which is worse.
Yes, your original use of 'nor' is similar to 'neither ... nor'. The "neither" part would have been stated in a previous sentence. However, the word neither was probably not used. Instead, the previous sentence would have been a negative one (or had a definite negative sense).