When you upgrade joomla to 1.0.13, make sure that you have CB 1.1 running then also check that file includes version.php gets upgraded too.

Some people "customize/rebrand" joomla with that file, and don't upgrade it.

Now CB checks for password method to apply with joomla/mambo version, and it's using info from that file.

Also make sure that all files get upgraded. If needed do a backup then a full overwrite with a full and fresh joomla 1.0.13 copy and quickly remove installation folder.

Also for backend issues, make sure to apply official joomla patch available here and to check for known problems in the 1.0 upgrade forum, as well as to check compatibility with other extensions.