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.