Unfortunately, I have no way of bringing that list into the laptop pc I'm
currently typing this forum reply on.
No USB thumb drive?
Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8101E/RTL8102E PCI
Express Fast Ethernet controller (rev 05)
That is the Ethernet card (connection by cable).
Network controller: Broadcom Corporation BCM43142 802.11b/g/n (rev 01)
That is the Wifi card... and it does not run without proprietary firmware.
The best thing to do is to get a Wifi adapter from one of the two vendors
that guarantee it works with Linux-libre:
http://libre.thinkpenguin.com/ (using that URL, 25% of the benefits made on
your purchase are donated to the Trisquel project);
http://tehnoetic.com/
You could buy an internal card as well. However, depending on the brand of
your laptop, the mother may simply refuse to use it (DRM).