Finally after many attempts, the line below does what it should. Now I need to get the correct syntax to run it with alternate credentials.
objShell.Run("%SystemRoot%\system32\WindowsPowerShell\v1.0\powershell.exe -noexit -command\\net\Hartfiles\Install\Software\NewUser\Create2007Mailbox.ps1" + "'" + strCanonicalName + "'" + " " + "'" + strUser + "'")
All I want to do is launch the powershell shell (From a VBS script) as a different user.