One way maybe could be:
Make an empty and parent all objects to that empty.
With the delay actuator you could later ...
change the visibility of that empty (with children checked)
Animation can be played with the Action Actuator:
Did you check in the Properties tab, on the icon that looks like a printer, at the Post Processing section if either the Compositing or Sequencer box is checked?
The Compositing outputs the Compositor Editor or the 3D Viewport camera while the Sequencer outputs the VSE/Video Sequencer.
User error (unsurprisingly). Turns out I'd managed to fill my hard drive. Blender was just giving up when it hit the limit.
In my opinion, this really should have resulted in a visible error message that would have helped identify the problem, but at least now I know what to look out for.
The End Frame is set to 250 frames, increase this value (bottom right of your Timeline editor), otherwise it will only play 10 seconds. You can also display seconds rather than frames: enable View > Show Seconds.
The issue was a codec issue. In DV I exported with a GoPro CineForm codec RGB-16 bit, and it worked. I read the available codecs in the blender docs, and that one isn't even listed there, but I bet it's probably using one of the others listed, probably open source or something.