Ubuntu has officially dropped support for Ubuntu 10.10, so apt-get will no longer work.
To fix this,
# nano /etc/apt/sources.list
NOTE: Any text editor can be used. vi and nano are the two popular ones.
Change all "deb http://archive.ubuntu.com/ubuntu" to "deb http://old-releases.ubuntu.com/ubuntu"
Basically, change 'archive' to 'old-releases', then run apt-get update.
Your problem should now be resolved.