Install OS on Galaxy S4 w/ broken screen

I have an Samsung Galaxy S4 with a broken screen (no touch input and no visual output); it's been sitting in my closet for months, but it still charges & boots. Now, I want to put it to good use by installing a new OS (e.g. Ubuntu and/or Android) and turning it into a server on my home network (the battery would act as a convenient UPS). However, since the screen is broken I can't access any menus and can't give it any input. Is there a way to access this phone to perform a fresh OS install (e.g. via USB)? *Note: This question was originally posted on SuperUser, but migrated here because it was off-topic for that community.*