[Short answer] Yes remove fans. Flat screen TVs are mostly Peripheral High Grade. Laptop motherboards have a class of their own.
[Long answer] First I'm not an expert, but I have been working with computers for about 30 years and scrapping e-waste for around 15 (scrapping in general since 1988). Most of what I know about e-scrap has come from reading posts on this message board. Each scrap yard will have different terminology and Boardsort has the most comprehensive list of classifications I have seen yet.
Check out this thread. The second post gives an explanation of the categories and the third has the categories listed with links to previous posts with answers. This is where I get most of my experience with grading boards.
viewtopic.php?f=3&t=21765Here's another post that gives details on what to remove and not to remove. Also info on how to post a good question that will help get more response.
viewtopic.php?f=4&t=19156Feel free to ask questions and post pictures. As long as you follow the guidelines and be patient for an answer you won't bother anyone.