Have you got any debug lines to ensure that the script is running?

How about adding some status information, so that you know that the INI file is being read?

I'd change the INI file path, as the reference will almost certainly fail.

This version will set the INI file path to the correct place, and display comments as it is doing the mapping:

; Set location of ini file, depending if we are logging on or testing.
If @LOGONMODE
        $sGroupINI=@LSERVER+"\NetLogon\groups.ini"
Else
        $sGroupINI=".\groups.ini"
EndIf
 
For Each $group in Split(ReadProfileString($sGroupINI,'',''),Chr(10))
        If $group AND InGroup($group)
                For Each $drive In Split(ReadProfileString($sGroupINI,$group,''),Chr(10))
                        If $drive
                                $resource=readprofilestring($sGroupINI,$group,$drive)
                                $rc=execute('$$resource='+$resource)
                                Use $drive+':' /delete /persistent
                                "Mapping drive "+$drive+": to "+$resource
                                Use $drive+':' $resource
                                If @ERROR
                                        " ***ERROR***" ?
                                        "["+@ERROR+"] "+@SERROR ?
                                Else
                                        " OK" ?
                                EndIf
                        EndIf
                Next
        EndIf
Next