Short buzz noise on startup

My HP Pavilion emits a soft, short, buzz noise on startup when “awakening” from sleep and randomly on keystrokes. I’ve updated the BIOS and cleaned the vents (to the extent I can find them). HP has been useless – I’m just out of warranty, and the Blog response has been ridiculous (a drop of oil on the fan?) to mostly just ‘crickets’. I’m not looking for a miracle, just some direction. Do you have any suggestions?