Well as you are new in Exchange Web Services ( EWS ) , I will suggest you to read this series of articles form Brij [ Check For Microsoft Exchange Section ] .
If you check the Second Article,
Programming With Exchange Server 2007 (EWS) - Part 2
], there is a section "
Getting the Count of the Unread Items in a Specified Folder
Which will do the job for you.
Hope this will help !