Wireless doesn't work for me in Lubuntu but does in Puppy?

Question

I am new to GNU Linux. I have been having trouble getting wireless working on my installed system of Lubuntu 11.10. It sees my WPA network but cannot connect even when I remove the password.

Looking around for a different distro that might replace it, I was amazed to find that Puppy was able to connect to my wireless network without trouble, running off a USB stick. So this makes me think that my Lubuntu wireless problem might be fixable so I don't have to have the major hassle of backing up all my documents etc before installing a different distro to the laptop. Can anyone suggest some steps that might help me to fix wireless on Lubuntu, perhaps using the fact it works with Puppy? Thanks.

Rob

EDIT: (Thank you both for the advice and link on making the question more useful. Hope this is better...)

(PS. WEP doesn't work either; rebooting doesn't help)

Here is the output for Lubuntu (wireless network on; wired ethernet connection to laptop unplugged):

> lspci -nn
...
10:00.0 Network controller [0280]: Broadcom Corporation BCM4311 802.11b/g WLAN [14e4:4311] (rev 02)

> ifconfig
eth0 Link encap:Ethernet HWaddr 00:1c:c4:c9:80:75
UP BROADCAST MULTICAST MTU:1500 Metric:1
RX packets:0 errors:0 dropped:0 overruns:0 frame:0
TX packets:0 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:0 (0.0 B) TX bytes:0 (0.0 B)
Interrupt:22 Memory:e4600000-e4620000

eth2 Link encap:Ethernet HWaddr 00:1a:73:e6:b6:16
inet6 addr: fe80::21a:73ff:fee6:b616/64 Scope:Link
UP BROADCAST MULTICAST MTU:1500 Metric:1
RX packets:0 errors:0 dropped:0 overruns:0 frame:0
TX packets:0 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:0 (0.0 B) TX bytes:0 (0.0 B)
Interrupt:17

lo Link encap:Local Loopback
inet addr:127.0.0.1 Mask:255.0.0.0
inet6 addr: ::1/128 Scope:Host
UP LOOPBACK RUNNING MTU:16436 Metric:1
RX packets:400 errors:0 dropped:0 overruns:0 frame:0
TX packets:400 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:0
RX bytes:31840 (31.8 KB) TX bytes:31840 (31.8 KB)

Btw, on Puppy, ifconfig gives:
lo Link encap:Local Loopback
inet addr:127.0.0.1 Mask:255.0.0.0
UP LOOPBACK RUNNING MTU:16436 Metric:1
RX packets:120 errors:0 dropped:0 overruns:0 frame:0
TX packets:120 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:0
RX bytes:9104 (8.8 KiB) TX bytes:9104 (8.8 KiB)

wlan0 Link encap:Ethernet HWaddr 00:1A:73:E6:B6:16
inet addr:192.168.0.100 Bcast:192.168.0.255 Mask:255.255.255.0
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:17375 errors:0 dropped:0 overruns:0 frame:0
TX packets:16352 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:17577062 (16.7 MiB) TX bytes:3587630 (3.4 MiB)

(Back to Lubuntu:)
> sudo lshw -class network
[sudo] password:
*-network
description: Ethernet interface
product: 82562GT 10/100 Network Connection
vendor: Intel Corporation
physical id: 19
bus info: pci@0000:00:19.0
logical name: eth0
version: 03
serial: 00:1c:c4:c9:80:75
capacity: 100Mbit/s
width: 32 bits
clock: 33MHz
capabilities: pm msi bus_master cap_list ethernet physical tp 10bt 10bt-fd 100bt 100bt-fd autonegotiation
configuration: autonegotiation=on broadcast=yes driver=e1000e driverversion=1.3.10-k2 firmware=1.1-2 latency=0 link=no multicast=yes port=twisted pair
resources: irq:43 memory:e4600000-e461ffff memory:e4620000-e4620fff ioport:4020(size=32)
*-network
description: Wireless interface
product: BCM4311 802.11b/g WLAN
vendor: Broadcom Corporation
physical id: 0
bus info: pci@0000:10:00.0
logical name: eth2
version: 02
serial: 00:1a:73:e6:b6:16
width: 64 bits
clock: 33MHz
capabilities: pm msi pciexpress bus_master cap_list ethernet physical wireless
configuration: broadcast=yes driver=wl0 driverversion=5.100.82.38 latency=0 multicast=yes wireless=IEEE 802.11bg
resources: irq:17 memory:e4000000-e4003fff

> rfkill list all
0: brcmwl-0: Wireless LAN
Soft blocked: no
Hard blocked: no
1: hp-wifi: Wireless LAN
Soft blocked: no
Hard blocked: no

The output from
dmesg
dmesg | grep -i firmware
cat /var/log/udev
cat /var/log/dmesg
cat /var/log/Xorg.0
ls -lrt /var/log
is here if required! (pardon my ignorance)

Further (more than a month later):

Well, finally I tried the suggestions on that page suggested by fossfreedom, and pages linked therein (did things one at a time with reboots where suggested):

did the suggested uninstalls (bcmwl-kernel-source package),
did the installs (firmware-b43-installer and b43-fwcutter packages),
commented out the blacklist (in /etc/modprobe.d/blacklist.conf)

etc, etc, and variations suggested.

Wireless still doesn't work.

Out of interest, here's what I get with the following. Is the "access denied" significant/suggestive? Does anyone kind, lucid and patient, have any other ideas?

> lspci -vnn -d 14e4:  

10:00.0 Network controller [0280]: Broadcom Corporation BCM4311 802.11b/g WLAN

[14e4:4311] (rev 02)
Subsystem: Hewlett-Packard Company BCM4311 802.11b/g Wireless LAN Controller

[103c:1375]
Flags: bus master, fast devsel, latency 0, IRQ 17
Memory at e4000000 (64-bit, non-prefetchable) [size=16K]
Capabilities:
Kernel driver in use: wl
Kernel modules: ssb

Also,

modprobe -r wl
FATAL: Module wl not found.

Another point: in Additional Drivers, the proprietary driver is still shown but is not active. Couldn't see how to remove it (only inactivate it). Neither worked (active or inactive).

My PC-ID of [14e4:4311] is supported according to this page: http://wireless.kernel.org/en/users/Drivers/b43

I don't grok at all what's going on. Not even the basics. Did at one point but am so befuddled now that I need a holiday. It's clear this distro was a bad choice for my level of non-expertise (will inform the friend who suggested it but uses something else; feel like a guinea pig).