dell latitude d51 wifi card lscpi
 

Sorry, I am a newbie and I am starting to think that I am terribly useless as well. I have been fighting with this laptop for about 4 hours now.
My lspci says

00:00.0 Host bridge: ATI Technologies Inc RS690 Host Bridge
00:01.0 PCI bridge: ATI Technologies Inc RS690 PCI to PCI Bridge (Internal gfx)
00:05.0 PCI bridge: ATI Technologies Inc RS690 PCI to PCI Bridge (PCI Express Port 1)
00:06.0 PCI bridge: ATI Technologies Inc RS690 PCI to PCI Bridge (PCI Express Port 2)
00:12.0 SATA controller: ATI Technologies Inc SB600 Non-Raid-5 SATA
00:13.0 USB Controller: ATI Technologies Inc SB600 USB (OHCI0)
00:13.1 USB Controller: ATI Technologies Inc SB600 USB (OHCI1)
00:13.2 USB Controller: ATI Technologies Inc SB600 USB (OHCI2)
00:13.3 USB Controller: ATI Technologies Inc SB600 USB (OHCI3)
00:13.4 USB Controller: ATI Technologies Inc SB600 USB (OHCI4)
00:13.5 USB Controller: ATI Technologies Inc SB600 USB Controller (EHCI)
00:14.0 SMBus: ATI Technologies Inc SBx00 SMBus Controller (rev 14)
00:14.1 IDE interface: ATI Technologies Inc SB600 IDE
00:14.2 Audio device: ATI Technologies Inc SBx00 Azalia (Intel HDA)
00:14.3 ISA bridge: ATI Technologies Inc SB600 PCI to LPC Bridge
00:14.4 PCI bridge: ATI Technologies Inc SBx00 PCI to PCI Bridge
00:18.0 Host bridge: Advanced Micro Devices [AMD] K8 [Athlon64/Opteron] HyperTransport Technology Configuration
00:18.1 Host bridge: Advanced Micro Devices [AMD] K8 [Athlon64/Opteron] Address Map
00:18.2 Host bridge: Advanced Micro Devices [AMD] K8 [Athlon64/Opteron] DRAM Controller
00:18.3 Host bridge: Advanced Micro Devices [AMD] K8 [Athlon64/Opteron] Miscellaneous Control
01:05.0 VGA compatible controller: ATI Technologies Inc RS690M [Radeon X1200 Series]
03:01.0 CardBus bridge: O2 Micro, Inc. Cardbus bridge (rev 21)
03:01.4 FireWire (IEEE 1394): O2 Micro, Inc. Firewire (IEEE 1394) (rev 02)
09:00.0 Ethernet controller: Broadcom Corporation NetXtreme BCM5755M Gigabit Ethernet PCI Express (rev 02)
0b:00.0 Network controller: Broadcom Corporation BCM4311 802.11b/g WLAN (rev 01)

ANd I do not have a clue as why does it does not work.

Any help will be appreciated.

thank you.

Assuming that you are using Ubuntu (according to your status icon, the distribution you use is information that needs to be in any thread where you ask for help), just open the "Additional Drivers" program and let that install the drivers for you.