Ubuntu – WI-FI doesn’t work (Hard Blocked)

Yesterday I installed Ubuntu 12.04 for the first time (I've always been a Windows user) as I was at the office and I had the Ethernet connected.

At home I only use WI-FI. When I started Ubuntu it didn't connect or try to connect with any network.

By google, I found the command rfkill and these are the results:

0: hci0: Bluetooth
    Soft blocked: no
    Hard blocked: no

1: brcmwl-0: Wireless LAN
    Soft blocked: no
    Hard blocked: no

2: dell-wifi: Wireless LAN
    Soft blocked: yes
    Hard blocked: yes

3: dell-bluetooth: Bluetooth
    Soft blocked: no
    Hard blocked: no

Well, the WI-FI is blocked by hardware, so I tried the command rfkill unblock 2 and it didn't work. As I didn't know even my Broadcom model, I found lspci and the result for the WI-FI is:

0e:00.0 Network controller: Broadcom Corporation BCM4312 802.11b/g LP-PHY (rev 01)

My laptop is a Dell Vostro 1520 with WinXP also installed.
Thanks for the help!

PS: It also may help that when I enter System Settings > Network (it may be different, my Ubuntu is in Spanish) "Airplane Mode" is connected. When I try to unlock it, it goes to its original place after I close that window and open it again and when I reboot.

Update added from comment to an answer

The Broadcom "Additional Drivers" are turned on and enabled.