Slackware 10.0 is a tad outdated. You're wise to upgrade to a recent sendmail release, but I hope you took the package from the slackware-10.0/patches/packages directory and not from slackware-current?
The "noarch" package contains the necessary configuration files for Sendmail. "Noarch" means the package does not depend on a certain processor architecture, but can be installed on any computer.
Something does not seem right after installing your sendmail package - the /var/spool/mqueue and /var/spool/clientmqueue directories (these two appear in the error messages) should have been created.
Try creating them yourself:
mkdir -p /var/spool/mqueue
chown root:mail /var/spool/mqueue
chmod 700 /var/spool/mqueue
mkdir -p /var/spool/clientmqueue
chown smmsp:smmsp /var/spool/clientmqueue
chmod 770 /var/spool/clientmqueue