I received this error (mapiexceptionnetworkerror: unable to make connection to the server (hr=0x80004005, ec=2423)) when attempting a move mailbox request from Exchange 2003 to Exchange 2010 after a little digging it appears both servers need to be able to talk to each other using the short name and the FQDN in my case the Exchange 2010 server couldn’t ping the Exchange 2003 server using the FQDN but it could the short name.
In my case it turn out DNS service had stopped when i restarted it everything worked fine, if this isn’t the case in your situation you could always add an entry into your DNS zone or create an entry in your host file to get around the problem.