Video was not copied because video format is not supported by the ipod

I am completely out of ideas, please SOMEBODY help me!!! Thank you in advance!!!

I purchased and downloaded (directy from iTunes) new T.V. shows. Unfortunately, I didn't realize that the format I was downloading them in were not supported by my iPod Classic 160GB Black (Model A1238). Now, when I sync my iPod, I get an error message for each video:

(Video name) was not copied because video format is not supported by the ipod

I CAN watch the videos directly from my computer.

I have read every blog/forum/support entry I can find, and nothing works for me. When I click the "Advanced" button within iTunes, the "Create iPod or iPhone version" option is grayed out! I have attempted to use many different video converters to downsize the video, but they are either:

-trials that wont do the whole video (or put a watermark at the bottom) - and I haven't even tried them, as I'm not going to spend ANOTHER $30 just to get T.V. shows that I bought from Apple to work on a product I also bought from Apple

OR

-failing to convert the file - they look at the video file and fail because the file is encrypted (or some nonsense) - I got this from Handbrake and a couple others.

I called Apple, but my new iPod Classic isn't new enough (3 days outside my 90 day support), and they won't help me. Can anybody please point me in the right direction? Again, they are iTunes downloaded videos (T.V. shows) downloaded directly into iTunes, Sync'd directly to an iPod - but their own Conversion option is grayed out, and other video converters don't appear to play nicely with the downloaded files! Ahhhh! HELP ME PLEASE!!! Thank you so much for taking the time.