iPod Problem, videos not showing on ipod

Intro: I was givven an ipod with the following problem: the video playlists are showing as music playlists in the ipod. When you play any of the videos in such playlists on your ipod you end up with only the sound and not the video.

Facts: when using itunes to add videos, and you create a playlist using only videos, eventhough this list might show up as a playlist in your itunes, when you sync your ipod that list should not show in the music playlists but in the video playlist of your ipod.
I have no idea how this problem actually came into exsistence, but this is the second time I hear about it, and if anyone has an idea of the problem itself and an easier way of fixing it that what I am going to be doing please let us all know.

Procedure:
Here is what I am going to be doing:
1- BACKING UP the ipod: I am going to try to move all the info of the problem ipod to my ipod and do the test from there since I don't want the problem ipod to loose any info.
2- USING iGadget to transfer music from ipod to itunes: I need to enable syncing to my itunes after I mirror the problem ipod to mine.
3- CHECKING: I need to see if re syncing will solve the problem.