Quite possibly. These issues are often quite complex, and you thus should probably contact an IP attorney in your area (there are quite a few in the bay area) and hire one that you like whom you feel will do the job you need them to do.
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No one can provide you with any actionable advice without knowing more facts. Assuming you own the copyright in the video, and registered that copyright with the Copyright Office, then perhaps you have a claim. I assume the late night TV show, however, was a comedy show. If it was and if it used part of your video as satire or parody then it quite likely could do so lawfully under the fair use doctrine without any compensation to you. Which is what they've all been doing for many, many years now. Speak with your own copyright attorney.
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There is no way to tell without additional facts and information. You should speak with an intellectual property attorney who can review how the late night cable show actually used your footage. The late night show's usage may potentially be a fair use.
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Probably you have NO case, as most late night show footage is for comedic purposes, for commentary, for parody, or for news reporting. The networks are very savvy on what is fair use and what is not. The fact that the clips were altered and titles were changed suggests that the network lawyers did what was needed to fall within fair use guidelines. You could take your comedy and a tape of the footage shown on Letterman, Leno, Fallon, or whoever to a copyright attorney for a quick consult, but my guess is you would at most be talking about a few hundred dollars in potential damages, and more likely zero damages. That will not make a viable case for copyright infringement, as for that you will need more like a few hundred thousand dollars of potential liability to even consider filing.
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