Somehow broke logger, thereby breaking everything

Hi Peter

A symlink is not a real file, it's a reference for another file. I am sure google can find you some very nice and better explanations about them ,o)

In your PM you mentioned "weird code" when you did "vi logger".
It looks like the symlink was not properly removed. Did you get a prompt "rm: remove symbolic link `logger'?" and answered "y" to it?
that would mean you may have edited busybox, and that's bad news (busybox is the binary for some very important commands).

You should get a "logger" [New File] prompt on the bottom of the vi screen (instead of "logger" x lines, x characters and loads of stuff, starting with ^?ELF -> meaning you are editing a binary executable; <ESC> :q! will get you out of vi without saving)

can you try running to make sure you did not mess with it:
busybox --list

you should get a list of apps that your busybox supports, including logger and vi.