I have recently had the same problem; to clarify:

I am fully able to download both music and video files, however, I am able to play only the music files through the limewire media player. I am unable to play or preview any kind of video files.

There are two ways I managed to resolve this problem and possibly may help you:

1) Any new media software can affect the functionailty of Limewire and your current media player [eg Windows Media Player], therefore if you have recently downloaded any new media software; try removing the software from your computer and restart your system [After this, limewire should work]

2) If you are running windows; make sure you install any updates for your computer as these can effect the functionality of your computer.

Good Luck!