LiveCD with running ssh server

sysrescuecd does have a running ssh daemon, but you would need to specify the root password in the startup options - with the default settings you would end up with an empty password and thus the account would be exempted from remote login.

You can create an Ubuntu LiveCD with an appropriately configured SSH daemon, users & passwords (or better, SSH keys!), etc. -- This may take a bit of work, but it guarantees that you'll have a LiveCD with all the tools you need to make a backup of the server (via simple tar, dump, dd, or any other mechanism you can fit onto a CD).

I use the PLD Rescue CD. It's pretty compact, but includes most of the Linux (and some Windows) utilities I need. I think sshd is enabled upon boot, but you'll need to simply assign a password of your choice. The default is "pld".