I don't know that there's a way that Microsoft intended to let that happen. As you describe the issue, it would make much more sense to move all mailboxes, public folders, GAL generation, etc away from the older Exchange server and then decommission it.
That said, removing all Receive Connectors and Send Connectors from the Exchange server, would effectively stop it from receiving or sending mail.
You could still delete mail by logging into an OWA or Outlook mailbox with Full Access permissions, though. It's possible to set permissions for a mailbox to read only, though. link text
So the next step would be to create an account that has read-only permissions to all mailboxes. A command such as the following should do the trick:
get-mailbox -server "readonlyexchangeserver" | add-mailboxpermission -accessrights ReadPermission -user ReadOnlyUser
Then remove all access permissions for the original users using the following command (syntax here link text)
get-mailbox -server "readonlyexchangeserver" | set-casmailbox -activesyncenabled $false -imapenabled $false -mapienabled $false -owaenabled $false -popenabled $false
You could also remove each user's permissions to their assigned mailboxes instead of the previous command.
If you wish to have a much easier time of this, you could simply export each mailbox into a PST, mark them as read-only, and review the mailboxes from there.