Support for Ubuntu 7.10 ended in April 2009 and the incremental upgrade method is only available from one release to another. There are two options I can think of however. The first would be to upgrade to Ubuntu 8.04 LTS and then upgrade to Ubuntu 10.04 LTS (still in development)
Here are the steps for using this method. First you would need to replace all the default Ubuntu 7.10 repositories
Open a Terminal and submit the following command
sudo gedit /etc/apt/sources.list
Delete all the default Ubuntu 7.10 (gutsy) repositories and replace them with these
deb http://old-releases.ubuntu.com/ubuntu/ gutsy main restricted
deb-src http://old-releases.ubuntu.com/ubuntu/ gutsy main restricted
deb http://old-releases.ubuntu.com/ubuntu/ gutsy-updates main restricted
deb-src http://old-releases.ubuntu.com/ubuntu/ gutsy-updates main restricted
deb http://old-releases.ubuntu.com/ubuntu/ gutsy universe
deb-src http://old-releases.ubuntu.com/ubuntu/ gutsy universe
deb http://old-releases.ubuntu.com/ubuntu/ gutsy-updates universe
deb-src http://old-releases.ubuntu.com/ubuntu/ gutsy-updates universe
deb http://old-releases.ubuntu.com/ubuntu/ gutsy multiverse
deb-src http://old-releases.ubuntu.com/ubuntu/ gutsy multiverse
deb http://old-releases.ubuntu.com/ubuntu/ gutsy-updates multiverse
deb-src http://old-releases.ubuntu.com/ubuntu/ gutsy-updates multiverse
After you have done this click save in the top left hand corner and close the window.
Back in the Terminal submit
sudo apt-get update
This will add the repositories to the Ubuntu 7.10 installation. Open the Update Manager and apply any updates that are suggested. DO NOT select upgrade to Ubuntu 8.04 LTS if you get a notification at this stage
Once you have applied updates Reboot your PC/Laptop then open Update Manager again
You will be notified that a (New Distribution Release 8.04) is available
https://help.ubuntu.com/community/HardyU…
Go ahead and select that. The system upgrader with a Broadband connection usually takes around half an hour I have found through experience
Once Ubuntu 8.04 LTS is fully installed Reboot after which it is time to upgrade from Ubuntu 8.04 LTS to Ubuntu 10.04 LTS
Press Alt-F2 then type update-manager --devel-release
This command will open the Update Manager
Check for new updates. Once you have applied updates Reboot then open Update Manager again
As before you will be notified that a (New Distribution Release 10.04) is available. Go ahead and run the upgrader once again.
The whole process should take around 1-2 hours with a Broadband connection
Ubuntu 10.04 LTS (Lucid Lynx) User Guide
http://ubuntuguide.org/wiki/Ubuntu:Lucid
Alternatively you have the option to directly replace Ubuntu 7.10 with Ubuntu 9.10 which will mean erasing the Ubuntu partition
Ubuntu 9.10 Download
http://www.ubuntu.com/getubuntu/download
The Perfect Desktop - Ubuntu 9.10 (Karmic Koala)
http://www.howtoforge.com/the-perfect-de…
Ubuntu 9.10 (Karmic Koala) User Guide
http://ubuntuguide.org/wiki/Ubuntu:Karmi…
Using either method backup your data before starting