Okay, I found a “solution”. When I open the video that is linked to the ELAN-file in VLC player and keep it open (I can pause the video in VLC but the player has to be running), then the video also works in ELAN. If I just open and close the video in VLC, it’s not working in ELAN.
In fact, I just saw that all the videos in ELAN are working regardless of which video I open in VLC player as long as there is a video in VLC. Opening the VLC player without any video doesn’t make ELAN videos work.
And opening .mpg or .mp4 in VLC works. If I open an .mp3 file, ELAN still shows a blue screen instead of a video
Edit: VLC has to be opened on external screen