I fixed the problem.
It required me to delete the Marigold Theme folder.
I was unable to delete the files myself, though. Probably because they were password protected.
I had the hosting company delete the folder for me.
After that the website still showed a blank screen, but I was able now to log into admin. It said that the working them was 2010 but something obviously was still wrong because the page didn’t work. So I activated another Theme and then that one showed up fine. I then reactivate 2010 and everything’s back as it should be.
