YouTube asked me to become a partner and monetize my account. However, on some of these videos, I do not own the rights. There are only some videos in my account that I would like to monetize, and I would like to monetize all new videos I'm going to upload as well.

Does this mean that I have to delete the "non-copyrighted" videos from my account ? I don't want to. Instead, I just want to make them "unpublished" and therefore not monetise them with AdSense. Could this save my account and prevent videos from being deleted ?

Or should I delete all videos on which I do not own the rights, and then accept the invitation from YouTube ?

* I already have AdSense account
* I already have monetized one YouTube video

Thank you.