Plug it into your tv and take note of some of the videos that appear, and some that do not. Connect it back to your laptop and see if it seems like a certain file type isn't working. For example, your tv may play .mp4 videos but not .avi or .mpeg. This can also happen with images or audio clips.
I may play a .mp3, but not a .wma or .wav. Or display a .jpg but not .png.
Do you have access to the owners manual for the TV? It will typically list what files it supports. (It may also list other properties like a max resolution for an image or video as well.)
You can also rule out the external hard drive by copying one video that you can see on your tv and one that you can't to a flash drive or another HDD. If the same videos are visible, it's likely your tv's limitations on file types, vs a hardware issue with the hard drive, flashdrive, etc.
What make and model is the tv?