I had no wireless connection. eth0 functioned but there was no eth1. I finally got it up but it disappears again after each reboot. My question is : "How can I make eth1 come up automatically?"
Hopefully, this text contains some clue, which is why I tell this long story, detailing the original situation and my actions.
ORIGINAL SITUATION :
Hardware :
lspci (extract)
05:00.0 Network controller: Broadcom Inc. and subsidiaries BCM4311 802.11b/g WLAN (rev 01)
08:00.0 Ethernet controller: Broadcom Inc. and subsidiaries BCM4401-B0 100Base-TX (rev 02)
inxi -nx
Network:   Card-1: Broadcom and subsidiaries BCM4311 802.11b/g WLAN
           driver: b43-pci-bridge bus-ID: 05:00.0
           IF: N/A state: N/A mac: N/A
           
           Card-2: Broadcom and subsidiaries BCM4401-B0 100Base-TX
           driver: b44 v: 2.0 bus-ID: 08:00.0
           IF: eth0 state: up speed: 100 Mbps duplex: full
           mac: 00:1d:09:b7:bf:6f
lshw (extract)
*-network
                description: Network controller
                product: BCM4311 802.11b/g WLAN
                vendor: Broadcom Inc. and subsidiaries
                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: driver=b43-pci-bridge latency=0
                resources: irq:18 memory:c0200000-c0203fff
                
*-network
                description: Ethernet interface
                product: BCM4401-B0 100Base-TX
                vendor: Broadcom Inc. and subsidiaries
                physical id: 0
                bus info: pci@0000:08:00.0
                logical name: eth0
                version: 02
                serial: 00:1d:09:b7:bf:6f
                size: 100Mbit/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=full ip=192.168.0.101 latency=64 link=yes multicast=yes port=twisted pair speed=100Mbit/s
                resources: irq:21 memory:c0300000-c0301fff
Software :
ip a
iwconfig 
iwlist eth1 s
sudo ifconfig eth1 up
ifconfig -a
sudo ethtool eth1
ifup eth1 (with or without sudo)
--- etc ---
All said nothing about eth1 or said "interface doesn't support scanning" or something like that.
dmesg | grep eth1 : gave nothing
I tried to edit /etc/network/interfaces but I didn't know what to write in it. I copied an example found online :
auto eth1
iface eth1 inet static 
  address 10.5.15.200
  netmask 255.255.255.128
  pre-up ifconfig eth1 hw ether AA:6F:78:UI:34:34
and (of course) it said
ifup
AA:6F:78:UI:34:34: invalid ether address.
Failed to bring up eth1.
The GUI tools :
wifi-radar didn't see any wifi network.
Network Connections (lubuntu) saw one, the one with no password, but only displayed its name.
I RE-INSTALLED THE DRIVER
Following the instructions here:
Installing Broadcom Wireless Drivers
Then I had to type
sudo modprobe -r b43
sudo modprobe b43    
sudo rfkill unblock all 
After that I tested with inxi -nx :
inxi -nx
Network:   Card-1: Broadcom and subsidiaries BCM4311 802.11b/g WLAN
           driver: b43-pci-bridge bus-ID: 05:00.0
           IF: wlan0 state: down mac: 00:1e:4c:82:78:25
           
           Card-2: Broadcom and subsidiaries BCM4401-B0 100Base-TX
           driver: b44 v: 2.0 bus-ID: 08:00.0
           IF: eth0 state: up speed: 100 Mbps duplex: full mac: 00:1d:09:b7:bf:6f
The wifi functioned.
After each reboot, eth1 disappears again and to get it up I have to retype :
sudo modprobe -r b43
sudo modprobe b43    
sudo rfkill unblock all 
It's much better than no wifi at all, but it's a bit tedious. What should I do, please?