Is there any solution for finding whole of a video using some of its snapshot or a clip of it?
If you want to search with Google, you can use searching by image in Google Images. It's possible that you will find what you are looking for, but it's not sure. I tested it now by making a screenshot of a "What if Money Was No Object - Alan Watts" video on YT and searching with this image - Google found this video. As you can see on my search results first result is the video I was looking for, but on Vimeo, not on YT. And there are also some other videos that have the same part, so the screenshot matches all of them, and there are also some not connected results, too. I think it highly depends of uniqueness of the screenshot and the video you're looking for.