I was having a similar issue in Ubuntu 12.04 with Thunderbird 12.0.1. At least in my case, the origin of the problem was two-fold:
the option "Default system sound for new mail" works only if sound effects are enabled in Ubuntu. If you want Thunderbird to play the default system sound from the Ubuntu theme, but do not want to enable the sound effects, just provide this path
/usr/share/sounds/ubuntu/stereo/message.ogg in the option "Use the following sound file".
whenever you change the path to the sound file, it is crucial to restart Thunderbird, otherwise it plays no sound at all.
My suggestion is therefore to select the sound file manually and restart Thunderbird. If it still doesn't work, I think you should file a bug report in launchpad, see here how. This might be a possible duplicate of this very old bug.
Note that the "Choose sound" menu has an hard-coded filter for wav files. In order to select an ogg file you'll have to specify the location explicitly by clicking on the pencil icon and providing the sound file location.