Apple is aware that Apple Video Player 1.6 becomes muted after installing Mac OS 7.6.1. This also happens with version 1.4 of Apple Video Player. It will be corrected in a future release, and posted to Apple Software Update sites.
To correct the situation, follow these steps:
1. Quit Apple Video Player.
2. Open the Monitors & Sound control panel (or the Sound Control Panel).
3. Select Mute.
4. Deselect Mute.
5. Close the control panel.
6. Launch Apple Video Player.
The software should now function normally.
Another workaround is to use Apple Video Player 1.4.2 which does not exhibit this behavior.