Make sure that you have highlighted the file and clicked the "Launch" button. Sometimes double-clicking doesn't work.

If its still a no go try going Tool->Options->Player and unchecking "Use LimeWire MP3 Player". This will make LimeWire use YOUR mp3 player (like Winamp, Windows Media, Real, etc). You'd probably want to do this because even when LimeWire's player does work, it tends to skip a lot. And do check those volume controls (double click speaker icon in bottom right)

Cheers