let CRON send emails through SMTP ( debian squeeze )
You need to reconfigure your exim4 configuration to be an internet mailer:
dpkg-reconfigure exim4-config
Use the instructions starting in section 2 of the Debian Exim4 readme at http://pkg-exim4.alioth.debian.org/README/README.Debian.html. Section 2.1.1.1 describes the different types of configuration.
You seem to have it set to "local delivery only; not on a network", that needs to be changed to one of the internet style mail servers, pick the one that works best for you. By your description, it sounds like you want "mail sent by smarthost; no local mail".