Win32::FileOp::ShellExecute( runasuser => 'theProgram.exe' );
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It will not let you specify the user to run the program under, it just displays a dialog box asking you to enter the credentials.

There is no way to pass the username&password to the ShellExecute API function. There is no way even with the ShellExecuteEx.

Seems you would need to call the CreateProcessAsUser function. It used to be available via Win32::AdminMisc, but you could call it yourself using Win32::API. Another option is to run the process through the "runas" utility. Run "runas /?" in the command prompt.