Talvez você tenha o apache sendo executado na mesma porta
e nginx não pode vincular o endereço porque já está em uso.
Para mudar a porta do nginx, dê uma olhada nesta resposta em stackoverflow
[1] link
Aqui há um exemplo no meu cachorrinho
marco@BeastFMM:~$ sudo service nginx start
Starting nginx: nginx: [emerg] bind() to 0.0.0.0:80 failed (98: Address already in use)
nginx: [emerg] bind() to 0.0.0.0:80 failed (98: Address already in use)
nginx: [emerg] bind() to 0.0.0.0:80 failed (98: Address already in use)
nginx: [emerg] bind() to 0.0.0.0:80 failed (98: Address already in use)
nginx: [emerg] bind() to 0.0.0.0:80 failed (98: Address already in use)
nginx: [emerg] still could not bind()
nginx.
marco@BeastFMM:~$ sudo /etc/init.d/apache2 stop
sudo: unable to resolve host BeastFMM
* Stopping web server apache2 apache2: apr_sockaddr_info_get() failed for BeastFMM
apache2: Could not reliably determine the server's fully qualified domain name, using 127.0.0.1 for ServerName
... waiting [ OK ]
marco@BeastFMM:~$ sudo service nginx start
Starting nginx: nginx.
marco@BeastFMM:~$ ps aux | grep nginx
root 7986 0.0 0.0 78976 1288 ? Ss 17:07 0:00 nginx: master process /usr/sbin/nginx
www-data 7987 0.0 0.0 79316 1708 ? S 17:07 0:00 nginx: worker process
www-data 7988 0.0 0.0 79316 1708 ? S 17:07 0:00 nginx: worker process
www-data 7989 0.0 0.0 79316 1708 ? S 17:07 0:00 nginx: worker process
www-data 7990 0.0 0.0 79316 1708 ? S 17:07 0:00 nginx: worker process