As mentioned by Crazyguy, there are a few pretty subtle ways to get donkey brain that you may be missing. However, there are a couple ways to reduce donkey brain as well, most notably, one of the spells in the spell book can reduce donkey brain a little with each cast. If you'd like specifics on those, let me know, otherwise I'll let you explore a bit more.
The path I took is as follows.
Look to the south and go to farm.
Go to barn
go to back of barn
go to back of barn
go to work shed
search left trash can and dig through clothes.
enter shed
look through toolbox
go to farmhouse
without knocking, and immediately running from her, return to the farmhouse.
Go to study
restore key
try restored key.