Hi,
Thanks for your reply. I have tried to sync again considering your suggestions.
1. Regarding photos, I just wanted to stressed that I could sync photos, so some of sync function is OK.
2. I have checked all the boxed available, I could not find anything that is wrongly checked both in itunes and ipod. Furthermore, the sync process works well with my other iphone and ipad which might indicate that itunes is working well.
3. Since the music and video files are playable in itunes, iphone and ipad, I consider that the files should compatible to ipod too. The files are mp3 and mov files, which should be compatible in ipod.
4. I checked settings> General>Restrictions too. Could not find anything wrongly checked.
5. After I clicked sync, I could see grayed music and video names that is contained in on the ipod, as depicted below. These files could not be played and not present in ipod.

I am considering this as a software problem than hardware problem as other apps are running quite well.
I would highly appreciate any suggestions.
Thanking you.