Thats because your private key is encrypted...
You can add your key to an ssh agent using ssh-add
or remove the passphrase (and with it the encryption) from the key using the following command:
ssh-keygen -p -f /root/.ssh/id_dsa -N ''
EDIT
Oh I just realized that you try to use your public key to authenticate... You want to use the private key there:
ssh -v -i /root/.ssh/id_dsa backup@webserver.com
And just to make absolutely sure, the content of the file id_dsa.pub
goes into ~backup/.ssh/authorized_keys
on the webserver. You can use the following command to do that automatically
ssh-copy-id -i /root/.ssh/id_rsa.pub backup@webserver.com