You manually configured Plesk 10 or an earlier version to change the Plesk HTTP and HTTPS ports from their default values (80 and 433) to custom values and then upgraded Plesk to version 11. If you then install Nginx through Parallels Installer, you will not be able to switch on Nginx in Plesk.
When you install Nginx with Parallels Installer, Nginx is configured to use the standard HTTP and HTTPS ports, 80 and 443. So, to make the system work properly, you should change the custom ports to these values. To do this, you should remove the corresponding Plesk database entries.
Remove the custom HTTP and HTTPS ports from the Plesk database by running the following command in the server shell:
MYSQL_PWD=`cat /etc/psa/.psa.shadow` mysql -uadmin -D psa -e "delete from misc where param='http_port' or param='https_port';"
# /usr/local/psa/admin/bin/httpdmng --reconfigure-all