Otherwise, there are various 3rd party utiltiies that will do it.
If you used Ghost (http://www.symantec.com/sabu/ghost/ghost_personal/), they include their Ghost Walker program that changes the SID. Almost all other imaging programs you purchase usually include a similiar utility.. check with the software you used to produce the cloning.
Network connectivity should not be impacted. But duplicate SIDS hold major security implications when running a Windows network in Workgroup mode or when depending on local computer accounts for security.
EP, glad to see you come back and tidy up...did want to ask a one day favor, I want to enhance my resume , was hoping you could make me administrator for a day, if so, take me right off since I won't be here to do anything, and don't know the slightest about the board, but it would be nice putting "served administrator osnn", if can do, THANKS