The problem: the computers [Xbox 360 and a Kubuntu 12.04.1 laptop] can't access Internet through a recently-installed desktopless Debian 6 laptop (which is wirelessly connected to a WLAN station) but addresses are successfully given by dnsmasq.

The attempts:

1.1) /etc/dnsmaq.conf conffed according to http://wiki.debian.org/HowTo/dnsmasq: add lines

interface=eth0
dhcp-range=192.168.0.50,192.168.0.150,255.255.255.0,12h

1.2) Follow http://www.cyberciti.biz/faq/rhel-fedora-linux-internet-connection-sharing-howto/ and use their script to setup iptables.

2) Follow the Ubuntu Internet Gateway Method (iptables) at https://help.ubuntu.com/community/Internet/ConnectionSharing recommended and which worked at Share internet in Linux.

The Debian laptop was rebooted many times and between each attempt, with and without the script auto-executing via /etc/rc.local.

While adding the iptables-restore command to that file I disabled the script.