Hey! I am glad unplugging your cable worked for you!
I know I had this problem when I was at school, so unfortunately I couldn't just unplug my router. I wanted to comment my fix for this issue so that other people with a similar situation to mine don't get extremely frustrated like I did.
1. Turn on your Apple TV.
2. Go to "Settings > General > Network"
3. click on your current network
4. Go to "Configure DNS" and select "Manual"
5. Your DNS is the collection of four three-digit numbers at the bottom of the page. Select your DNS and change each number to 008 (Write down your old numbers just in case!). Example: DNS 008.008.008.008
6. After you do this your Netflix should work just fine, and I believe that you may change your DNS back to its original state after a day or so, but I'm not sure.
I hope this helps!