The problem is caused by several things...
1. You don't have sharing of video enabled through WMP. It's a real easy fix as it just requires you to check the settings box to enable it.
2. Your video library database is corrupted and needs to be rebuilt. This is really easy to fix as well because all you have to do is tell WMP to rescan for media files.
3. You don't have WMP running on your desktop when you are trying to access the video from the 360. You must do that for it to work, otherwise you have access to only your music and photos.
My advice to you is to switch to the Zune software. It handles more file formats than the WMP for 360 streaming playback, has all of the WMP functionality, and it just works better. I have been using it over WMP for quite some time and Microsoft recommends it over WMP.