Actually – after an hour of looking and looking, but immediately after posting the above message – I indeed found another /wp-content/plugins directory in a folder in the root called “blog” with wierd entries from my actual blog folder. I deleted this folder and now the plugins manager works!
So all your struggles gossegotha showed me the way. Thank-you all.
No matter what I put in or take out of the /wp-content/plugins/ directory, nothing changes in the plugins manager list. Is it possible that my host has its own plugins directory? My blog is on my site which is hosted by dreamhost.