Do you send to 'root' etc, or firstname.lastname@example.org
the second should work as is,
but the first may need a rule change to work
or you may have an error in your LOCAL_RELAY macro in your config file.
The manual says ..
'Unless you specify otherwise in the LOCAL_RELAY macro, any address that is a username without any @host part is delivered using the 'local' delivery agent.'
it adds that even if LOCAL_RELAY points at another machine to handle local addresses, 'root' will ALWAYS be delivered on the local machine, so the fact that root's mail is NOT arriving, leads me to think you haven't specified a local delivery agent.
at your root prompt, type 'sendmail -bt' to enter rule checking mode, and get the '>' prompt
at this prompt, type =M to list the mailers loaded.
you should see entries for mailers .. 0 (program), 1 (file), 2 (Include0, 3 (Local), 4 (smtp), 5 (esmtp), 6 (esmt8), 7 (dsmtp), and 8 (relay).
Some may be excluded if thats what you specify in the config file, but Mailer 3 HAS to be there f local mail is to be delivered.
If it's not, re-edit the sendmail.mc file to include a line MAILER('local'), and recompile.