Done, but not solved: No proprietary drivers are in use on this system.
Appears only Broadcom STA wireless driver
This package contains Broadcom 802.11 Linux STA wireless driver for use with Broadcom's BCM4311-, BCM4312-, BCM4313-, BCM4321-, BCM4322-, BCM43224-, and BCM43225-, BCM43227- and BCM43228-based hardware.
If additional drivers didn't find it, then most likely there is not a proprietary driver available for your chip on Linux, either that or the kernel your running is too old to support the driver that accompanies that chip. You can try installing 'fglrx' but I doubt it's going to pick up the chip and may leave it unbootable.