I think in most cases there is no problem using copyrighted songs, you just won't be able to make money from your video. As far as I know, the worst thing that can possibly happen is that the video will be blocked, so that no one or only people living in certain countries will be able to watch it.

I personally think it only happened in Dieter's head, didn't Neil and Chris make fun of Modern Talking in the 80s?

"Rent" is on YouTube, actually.
https://youtu.be/-d0GARTk_Nk