HP website's support ticket management can be improved.
After I made the ticket for reporting the problem, 3 days later I received a packet with a CPU fan in there. Looks like somebody at HP thought that I could open my notebook and replace the fan myself... :)
However, it took few more days for them to acknowledge the real problem. Then they picked up the laptop and returned it after 9 days with a replaced motherboard.
I am happy to say that the exhaust fan now works without the special sound it was creating earlier.
I feel happy that I purchased the HP Care pack.. :)