"Then I previewed it (ctrl+enter) and everything was fine, but once I saved (or published) it, the movie didn't play anymore."
I get the previewed step, but I am unclear at how you were testing it once published. Did you simply open the SWF on the computer? Did you upload to a server and preview in the browser?
If on the browser, did you upload all of the necessary files? You need to upload the F4V as well as the skin SWF. Also, did you check that the server has the F4V MIME-TYPE? This is a problem now, despite most servers having the FLV MIME-TYPE automatically, the F4V is a newer type of file, and many servers aren't set up to serve them.
Also, check that the paths aren't hardcoded to your local drive in the FLA. They should be relative to where the SWF is.
While I'm in flash and import the movie - everything works well in preview mode, but once I save/publish it and THEN try to preview (still in flash), it won't play anymore. I also tried to open both SWF and HTML files, STRAIGHT from my HDD, but it's the same story. I don't even upload it to the server as it doesn't work.
If you saved the FLA after you linked up the video file, it is likely the paths are incorrect.
Try removing the component, and re-import the video into the saved file
You were right. First I saved the file and then I imported the movie. Then I saved it again, published it and everything works as it should.
Thank you very much for your time and help !
Not a problem, glad its working for you now.