It seems like several people are hitting this issue with nginx not starting. For me the problem was that apache2 was still running. The following steps worked for me to switch from apache2 to nginx.:
Check whether apache2 is still running. If so stop it.
systemctl status apache2
sudo systemctl stop apache2
See if nginx will start now
sudo systemctl restart nginx
systemctl status nginx.service
If nginx doesn’t start, try installing again:
sudo apt install nginx
sudo nginx -t
If nginx started successfully then go ahead and disable apache2
sudo systemctl disable apache2