WiFi device not starting with normal combination keys

Can you give the output of:

sudo lshw -C network; lsb_release -a; uname -a; dmesg | grep -i firm

Thanks

  This is the out of the above command:

*-network
       description: Ethernet interface
       product: BCM4401-B0 100Base-TX
       vendor: Broadcom Corporation
       physical id: 0
       bus info: pci@0000:08:00.0
       logical name: eth0
       version: 02
       serial: 00:1c:23:95:70:4f
       size: 10Mbit/s
       capacity: 100Mbit/s
       width: 32 bits
       clock: 33MHz
       capabilities: pm bus_master cap_list ethernet physical mii 10bt 10bt-fd 100bt 100bt-fd autonegotiation
       configuration: autonegotiation=on broadcast=yes driver=b44 driverversion=2.0 duplex=half latency=64 link=no multicast=yes port=twisted pair speed=10Mbit/s
       resources: irq:21 memory:c0300000-c0301fff
  *-network UNCLAIMED
       description: Network controller
       product: BCM4311 802.11b/g WLAN
       vendor: Broadcom Corporation
       physical id: 0
       bus info: pci@0000:05:00.0
       version: 01
       width: 32 bits
       clock: 33MHz
       capabilities: pm msi pciexpress bus_master cap_list
       configuration: latency=0
No LSB modules are available.
Distributor ID: Ubuntu
Description: Ubuntu 12.04.1 LTS
Release: 12.04
Codename: precise
Linux lucian-Inspiron-1501 3.2.0-32-generic-pae #51-Ubuntu SMP Wed Sep 26 21:54:23 UTC 2012 i686 athlon i386 GNU/Linux
[ 0.171724] [Firmware Bug]: ACPI: BIOS _OSI(Linux) query ignored
[ 0.206348] [Firmware Bug]: ACPI: No _BQC method, cannot determine initial brightness
[ 0.276017] pci 0000:05:00.0: BAR 0: trying firmware assignment [mem 0xc0200000-0xc0203fff]
[ 13.565676] [Firmware Bug]: ACPI: No _BQC method, cannot determine initial brightness

end quote
Thanks

Please run
lspci -vnn |more +/4311
and confirm that the chip we are talking about is not a 14e4:4313 (it should be 14e4:4311 or 12)
If not a 4313, then the below should fix you up.

With the Ubuntu 11.x releases, the proprietary Broadcom drivers stopped
working with the 4311 Broadcom chips (see bug 732677). However
your 4311 chip works fine with the open b43 driver, but you first need
to install its firmware -- easily done with a package install.
Remove the proprietary STA driver (and its configuration files which
suppress the working b43 driver) by reversing whatever you did to install them:
sudo apt-get purge bcmwl-kernel-source
and/or run additional-drivers and unselect the Broadcom STA driver

Check that your removal/deactivation above is complete:
all the lines with "blacklist b43" should have
been removed from all files in /etc/modprobe.d. These blacklist lines suppress
the b43 driver, so they must be removed -- just the exact "b43" and b43legacy
ones, leave the bcm43xx alone. Deal with any leftovers:
 sudo rm /etc/modprobe.d/blacklist-bcm43.conf
 gksudo gedit any-file-found-with-b43
   and delete or put a # at the beginning.

The proprietary firmware cannot be distributed with the release,so you
have to manually add it. Use a wired connection, and in a terminal:
   sudo apt-get update
   sudo apt-get install b43-fwcutter
and accept the offer to download the Broadcom files, which
will put the Broadcom firmware into /lib/firmware/b43.
If you don't get the offer to download, then purge the package
and try again:
   sudo apt-get purge b43-fwcutter
   sudo apt-get install b43-fwcutter

You can even use the open source firmware (which is what I use):
   sudo apt-get install firmware-b43-installer
but only one set of firmware is needed (and non-4311 users should
check for needing other versions of the firmware (like
firmware-b43-lpphy-installer). If both sets of firmware are
present, the proprietary set in /lib/firmware/b43 will be used.

With the firmware in place, NetworkManager may start scanning,
if not, manually load the b43 driver module, or just reboot.
 sudo modprobe b43

NetworkManager should start scanning and offer a list of possible
connection points within a few seconds.

Select your access point, select the correct encryption method, and enter
your key. If you are not broadcasting your ssid and it does not show up in
the list of access points, you might have to left click NetworkManager and
select the menu item "connect to hidden network", and enter your ssid. Next
boot, the connection should be automatic.