Just for your information, Debian 7.1.0 during installation says that computer needs rtl_mic/rtl8168e3.fw, which is in their non-free repository.
http://packages.debian.org/wheezy/firmware-realtek
At any case, wired connection works perfectly with Trisquel. This is the ethernet entry from lspci
Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168 PCI Express Gigabit Ethernet controller (rev 07)
Dispositivos 3G | 34 |
Acquisition cards | 34 |
Bluetooth | 58 |
Placas de rede | 173 |
Leitores de impressão digital | 11 |
Controladores de host | 170 |
Modems | 18 |
Notebook | 796 |
Printers | 127 |
Adaptadores RAID | 20 |
Scanners | 24 |
Leitores de cartão SD | 57 |
Placas de som | 143 |
Placas de vídeo | 343 |
Webcams | 132 |
Placas wifi | 234 |
TOTAL | 2374 |