Turned out it was something with the file system. It got corrupted, and after a while applications began to force close. So I had to do a full factory reset. Then I was able to install BLN.
However, it still didn't work under the stock Samsung S4 Mini firmware, even with the Vikinger kernel patch applied. I ended up installing CM11, which seems to work flawlessly with BLN.
Thanks for your help anyway.