The first step is to update /etc/apt/sources.list to the following:
deb http://old-releases.ubuntu.com/ubuntu/ feisty main universe
deb http://old-releases.ubuntu.com/ubuntu/ feisty-backports universe main
deb http://old-releases.ubuntu.com/ubuntu/ feisty-security universe main
deb http://old-releases.ubuntu.com/ubuntu/ feisty-updates universe main
deb http://old-releases.ubuntu.com/ubuntu/ feisty-proposed universe main
After I did this, I could run the following commands:
sudo aptitude update
sudo aptitude upgrade
sudo aptitude dist-upgrade
sudo aptitude install update-manager-core
sudo do-release-upgrade
However, the process had some errors. Some packages failed to download because, for some reason, the update-manager would insert an invalid URL into the sources list. Turns out this is a known issue.
I got around this by using the tip posted here. The site which I couldn't prevent from being checked for downloads (us.archive.ubuntu.com) did not have the files that I needed. I Googled the URL (minus domain name) find the URL elsewhere. After a few tries, I found that the following site had the files:
http://mirror.csociety.org/ubuntu/dists/feisty-backports/main/debian-installer/binary-i386/
I checked to see if this address could be fetched with an IP number:
Macintosh-7:~ olaf$ host mirror.csociety.org
mirror.csociety.org is an alias for csociety-ftp.csociety.org.
csociety-ftp.csociety.org has address 128.46.156.117
Now, armed with the IP, I tried the link:
http://128.46.156.117/ubuntu/dists/feisty-backports/main/debian-installer/binary-i386/
It worked! Almost there. Now, I needed to send all requests for us.archive.ubuntu.com to this address. So, I edited my /etc/hosts file and added the following line:
128.46.156.117 us.archive.ubuntu.com
Now, when I tried to run the release steps the correct packages were fetched, but I got a new error:
"While scanning your repository information no mirror entry for the upgrade was found"
I found the fix to this error here: http://andreasjacobsen.com/2008/12/
After fixing my /etc/apt/sources.list as described in this article, do-release-upgrade ran without complaints and I'm upgrading as we speak. :)