If you've checked the obvious, then you may be experiencing a known bug in Microsoft DirectShow (a component of DirectX). There is a known issue associated with certain MP3s that have extended meta data (ID3 Tags) embedded in them. If this only happens with a small number of your MP3s, you can usually get the sound to play by clicking on the forward step button (>) after pressing play. If this happens with most or all of your MP3s, then you may want to enable the built-in work-around (introduced in version 3.6).
To enable or disable this work-around, open the Program Options window, then press F12. A message will appear telling you that it is either enabled or disabled. Name Dropper will remember this setting the next time you run it. Please note that this work-around usually gets the sound working on the troublesome MP3s, but you may notice that the first second of the file gets cut off when playing from the beginning. This does NOT indicate a problem with the MP3, but rather it is a side-effect of the work-around.