New and horribly confused
 

Hi, I own a 2002 MINI Cooper S and the factory battery died two days ago. I just had it replaced today and everything works fine, however, when I turn the car off it continues to make that electric "buzzing" noise when the fan is still on. I don't know what to do. My friend who works on cars thinks that something is running on the power when it shouldn't be. I'm very worried that I'm gonna go out and start the car and it's either still going to make the noise or that it drained the battery. HELP ME PLEASE!