Currently I'm not at home at the desktop, so I'm unable to try what you suggested until later tonight. But here's what I've come up with as a possible solution. When I go to the drivers/download page on Dell for my computer, here's what's listed under network:
To me, it makes sense that the second option down (Broadcom LAN driver) is what I need. But again, I'm pretty illiterate. So, I downloaded it, and get the following folder, unzipped:
There are just too many options! The download was simple, but what - given the previous picture - do I need to install? Or, am I completely off line here with what I need to do?