MacBook Pro won't connect to Apple TV via AirPlay
I've seen similar questions/threads and tried everything short of reinstalling the MacBook's operating system, but nothing has worked. Here's the deal:
-I have a new MacBook and Apple TV (both new as of 2015). All software is completely up-to-date on both.
-All other devices (two iPhones, one iPad) connect to Apple TV, mirroring and otherwise, as they're supposed to, with no issues
-Everything (MacBook, Apple TV, modem, wireless router) has been restarted. No other connectivity issues in the house.
-Home sharing and iCloud are turned on (using the same account) on both Apple TV and MacBook.
-Firewall on MacBook is completely off.
YET when I click on the AirPlay icon and then "Apple TV" on my MacBook, I get a pop-up telling me "Could not connect to 'Apple TV'."
The weird thing is that I could at least get the Apple TV to mirror this MacBook's display a few months ago. Now- nothing.
Please help.
MacBook Pro with Retina display, OS X El Capitan (10.11.5), Apple TV tvOS 9.2.1 (13Y772)