The recommended action for anyone still running 7.10 is to use the do-release-upgrade command to (relatively) painlessly upgrade to a newer, supported version of Ubuntu (remembering to take a backup first, just in case). The one little catch with this solution is that without access to the package repository, you won’t be able to install the upgrade tool if you don’t already have it.
Fortunately, the Gutsy repository hasn’t been removed completely, it’s just relocated to old-releases.ubuntu.com.
If you're seeing things like this:
404 Not Found [IP: 91.189.88.45 80]
Err http://archive.ubuntu.com gutsy/restricted Packages
404 Not Found [IP: 91.189.88.45 80]
Err http://archive.ubuntu.com gutsy/universe Packages
404 Not Found [IP: 91.189.88.45 80]
Err http://archive.ubuntu.com gutsy/main Sources
404 Not Found [IP: 91.189.88.45 80]
Then this is your answer.