Dear Priyanka,
First of all keep in mind that HR is not personal assistant or secretary to anybody. If there's any problem HR professionals are to help the settlement.
Second, it clearly indicates the poor management, poor policy and conduct. (Discuss with management and develop a policy for behaviour and conduct).
You can't issue warning letter without prior authorization by Management and as your Director is not interested to take any serious action, you're not in position to react and if you do so, it'll blame on your personal revenge and will hit your profession.
No doubt many problems and conflicts crop ups while practicing Human Resources and a professional handles all the issues. (Keep in mind that conflicts can't be eliminated but can be minimized with good HR Practices.
In your case specially, it seems congestion of infrastructure. Normally in production units, there're no discussions allowed that may effect on someone's concentration and for that separate discussion rooms are designed. As IT is 100% dependant of 100% of concentration and for that just discuss with management to maintain a good environment that increase proficiency of employees.
In the last, I urge to understand the role of HR. Good HR have the qualities to design and implement the policies and administer all the issues before they reach on peak.
Best Regards,
SM Alam
Executive HR