If you have the TV series and not the movies you will be using theTVDB.com not themoviedb.org.
The series is listed here http://thetvdb.com/?tab=series&id=77098&lid=7
You need to name your files correctly to get infuse to find it correctly. I’m guessing that Miami.Vice.S01E01.mkv (or .avi or .mp4. or what ever your extension is) should get you close.
If you provide an example of exactly how your files are named we can probably get you in the ballpark so infuse finds it for you.
EDIT TO ADD:
I just created a test set of files for Miami vice following the naming conventions I stated above “Miami.Vice.S01E01.mkv” for the files and “Miami Vice” for the folder their in and Infuse found it without a problem.
As a side note what your seeing where you saw “Miami Vice: Brother’s Keeper (1984)” I believe is actually the right one since “Brothers keeper” is the episode name for the episode 1 and 2 pilots.