After Effects renders with no audio
The output file doesn't have any sound because there is no audio in the timeline that you are rendering.

The output format (MP4 vs. AVI) doesn't have any effect; both formats can contain an audio track or not. Checking the box to output audio only has any effect if there is already an audio track in the timeline. If there's no audio track, the output will have audio but it will be silent (as you're experiencing).

The solution is to add some audio file(s) to the project and then put it into your timeline.