Solved: Windows 7 on Sony Vaio Driver Problem

Hi!
I have something of a problem. Rather, my friend who I've been helping does. He recently bought a new laptop -- a Sony Vaio F series (model SVF15A18CXB), but very much dislikes Windows 8.
After a lot of fiddling around, we successfully uninstalled Windows 8, and then installed Windows 7.

The problem is, Sony seems to have only made drivers for this model specifically for Windows 8.
We've managed to find drivers for almost everything that needs a driver installed - Bluetooth, network card, audio, and so on - but we've not been able to find drivers for the Wireless LAN component (BCM43142 Wireless Network Adapter).

The specs of the computer can be found here, if it helps, and the drivers that work for Windows 8 on the Sony site here.

He's running Windows 7 Home Premium, 64 bit.
We've tried the official drivers, and done some searching for other ones, but haven't had any luck in getting the wireless working yet. At something of a loss about what to do, does anyone have any advice?
Is there any more information that would help narrow down our options?

Thanks!