I still consider myself a green Flash user, so I hope I'm using correct terms.
I wrote a simple script using a tutorial for Controlling the Timeline with AS 3.0. On my local machine it exported the SWF, the stop and buttons worked perfectly. To be able to share it with my students, I saved the FLA file to a server. I opened the FLA file to show the timeline and scripting, then did a CTRL+ENTER to generate a SWF and it plays through as if there isn't a STOP in Frame 1. When I MOVED that FLA file to the local drive, I was able to generate a SWF file from the local machine and it worked perfectly.
I can move a SWF to the server that was generated on a local machine and it will work, but I can't figure out what I need to do to the server to get SWF files to play correctly from there.
After installation, run the program and open the link to your swf or html file in the browser. Then switch back to the program. It should list all the files being loaded. In particular, look for any files in red (404 errors, file not found) and copy those missing files over to your server.
Hope that helps.
General notice: from now on, I would like to ask everyone to put [AS2] or [AS3] (corresponding to the version of actionscript you are using on your project) in front of their post titles when the question is actionscript related! Please help us help you faster. Thank you.