Welcome to the forums!
Have you looked at Device Manager to see whether or not there are devices with problems (they'll have exclamation points after the device name)? I'll bet there's a problem with your WIRED Ethernet interface, and it's going to show up as something with an odd looking name that will not have anything to do with "Broadcom."
It would also be helpful to know which iMac version you have. My own 2007 vintage (original) 20" Aluminum iMac has a Yukon Ethernet card, while its AirPort (wireless) card is by Broadcom.