Well, I'm not one of the expert responders who typically help and know more than me, but it sounds to me that the problem might be with the movie file itself! Being able to pause a movie in the presentation and restart it, and all at predetermined points, is very high on my wish list for a future Keynote release! But so far as I know, it's not possible yet!
But first check the following:
Select the movie and then unclick 'Start movie on click' at the bottom of the Format/Movie palette. This is an annoying default which makes every movie you bring into Keynote require a click to start rather, than starting after the slide transition.
Under the Repeat pull down above that, make sure it is not set to Loop or Loop back and Forth but is set to None.
Go to the Animate palette and click on Build Order at the bottom - check on the Build Order pane that there are no builds which might cause this. Delete all of them if there are.
As with many glitches, it's also worth restarting Keynote too.
But, as I said, I don't really think the problem is with Keynote. Several versions ago in the history of Keynote, you could export a presentation as a QuickTime movie and the resulting movie would have all the mouse pushes embedded so that it would pause at the appropriate places and restart. This way, you could export your presentation for PC users (who couldn't run Keynote) without the difficulties of sending them a PPT (fonts etc). I don't even know if Keynote can still do this! So it's perfectly possible to have a movie file with this stop/start capability built in.
Does it run normally in QT? If so, try and export it in another file format and see if that works.