Run automatically Noip2 when the machine is booted?

Two steps for you to solve this. Your script (/etc/init.d/noip2) should look like:

#! /bin/sh
# /etc/init.d/noip2

# Supplied by no-ip.com
# Modified for Debian GNU/Linux by Eivind L. Rygge <[email protected]>
# Updated by David Courtney to not use pidfile 130130 for Debian 6.
# Updated again by David Courtney to "LSBize" the script for Debian 7.

### BEGIN INIT INFO
# Provides:     noip2
# Required-Start: networking
# Required-Stop:
# Should-Start:
# Should-Stop:
# Default-Start: 2 3 4 5
# Default-Stop: 0 1 6
# Short-Description: Start noip2 at boot time
# Description: Start noip2 at boot time
### END INIT INFO

# . /etc/rc.d/init.d/functions  # uncomment/modify for your killproc

DAEMON=/usr/local/bin/noip2
NAME=noip2

test -x $DAEMON || exit 0

case "$1" in
    start)
    echo -n "Starting dynamic address update: "
    start-stop-daemon --start --exec $DAEMON
    echo "noip2."
    ;;
    stop)
    echo -n "Shutting down dynamic address update:"
    start-stop-daemon --stop --oknodo --retry 30 --exec $DAEMON
    echo "noip2."
    ;;

    restart)
    echo -n "Restarting dynamic address update: "
    start-stop-daemon --stop --oknodo --retry 30 --exec $DAEMON
    start-stop-daemon --start --exec $DAEMON
    echo "noip2."
    ;;

    *)
    echo "Usage: $0 {start|stop|restart}"
    exit 1
esac
exit 0

Then make it executable, i.e run

# chmod a+x /etc/init.d/noip2
# update-rc.d noip2 defaults

Here is a more straightforward way to approach this...

We are trying to mimic your regular user account issuing this command (assuming you followed No-IP's recommended setup instructions) ...

sudo noip2

The reason your regular user account (instead of your super user) needs to issue this command is because your regular user account has some No-IP-specific stuff that needs to be accessed when issuing this command. So to mimic issuing the command above as your regular user account with elevated privileges at startup, do the following...

Edit your super user's crontab by issuing this command...

sudo crontab -e    (choose your favorite text editor if prompted)

Add this line at the bottom of the file...

@reboot su -l <regular account username> && sudo noip2

Save the file and reboot your system. You will find that noip2 has been started properly.