Hi Matt,
Ran across a page that had a couple of suggestions that wouldn't have occurred to me, so they might be worth a try.
[link|https://votepair.org/why-brother-printer-wont-turn-on/|[SOLVED] Brother Printer won't Turn On: How to Fix it|new_window=true]
Here's a summary of their suggestions.
# Disconnect and Connect the Power Cable
# Check the Power Cable and Printer’s Power Button
# Clean the Printer
# Check the Cartridge & Print Head
# Disconnect the USB
Read through items 3 and 4; there's a little more to them than the title would suggest.
Let us know what happens!