Our intranet server using sendmail stopped delivering messages.
I found that the /var partition is filled up to 107%, possibly due to the extremely large /var/spool directory.
Please help me how to empty the message queue of sendmail so that it can be fit again, and the messages in the queue presently be preserved for future processing? (I.e. no mails should be lost).
Please be specific as I am a green newbie to sendmail, I do not even know how to start and stop it.

Usually this happens when people (users) leave a copy of their messages on the server. We used to have this problem all the time.
Another cause is the /var/log/ directory. If you check here you will find log files such as "messages.<number>" or "secure.<number>". These will be the older log files and can be deleted with no worries. If you do not delete them they will fill up your /var partition and stop services that depend on them.

DO NOT delete logs not followed by ".<number>"! You will need this info at some point!

to restart any service, use "/etc/init.d/<servicename> restart"
to stop, it's "/etc/init.d/<servicename> stop"
etc, etc....

cd /var/spool/mail
type ls -l and look for any really large files, these will be users not taking their mail off the server. Just copy the files somewhere else for later processing to clear up the space. (The file will be in MBOX format, and can at any time be renamed to a new user for processing, or opened with Pine or Mutt or many other Linux Mail Agents)