Running batch file as admin from Test Complete

If you have the option, you could always run TestComplete as an administrator.  I don't know if this is a security/policy issue for you.  When you do so, then anything you execute within TestComplete is run with that privilege level.  

That said, rather than using a batch file, you could always use the WshShell Object to execute a command line to start/stop as service.  This is what I've used in the past and is much easier to keep track of than the location and contents of batch files.  See https://support.smartbear.com/testcomplete/docs/reference/program-objects/wshshell/index.html