Did you insert the movie to the Stage before or after you saved the file?
What I see happen a lot is that people open a brand new Flash file, insert a video, then save the file. It works perfect locally, but not on the server. This is because, when inserting a video into an unsaved document, Flash automatically creates an absolute path to the video on the computer. Since that path is not available on the server, the video doesn't load.
To remedy - open the FLA, select the video object on the stage and go to the "Parameters" panel. Here you will see a list of attributes for the video. In the "source" attribute, you will see a path to a location on your computer ("C:/Documents and Settings/..../video.f4v" or "D:/My_Files/project/video.f4v" or some such). Change this to be a relative path (just "Sequence 01_1.f4v"), re-export and re-upload the SWF.
For future reference, you can avoid this by saving the FLA before importing a video. If the file is saved, Flash will use a path relative to the location of the FLA on your computer, rather than the absolute path it needs to work with an unsaved project.
