Do you mean that you also have problems with MySQL? As @jdrios mentioned in previous posts, the MySQL database doesn't depend on the machine IP.
Could you try to to log your server via SSH (you can do it following this guide), and then execute the commands below?
sudo /opt/bitnami/apps/wordpress/bnconfig --machine_hostname YOUR_NEW_IP
sudo /opt/bitnami/ctlscript.sh restart
Please note that you have to change YOUR_NEW_IP with the new assigned static IP address.
If you continue running into problems. Could you paste here the Apache and MySQL logs after trying start them? You will find then at: