Hi Harm,
In fact card is seen and connection to ADSL modem is well established. Ping 192.168.1.1 goes too.
Only no Internet available as issue so apt gives a lot of message error while installer is running.
As I'm still busy with new work, new house and moving every weekend between France and Belgium not so much time to test 
That looks like a DNS error to me.
If you can i.e ping 8.8.8.8 (google) than you do indeed have a connection and is that your problem.
If you can't ping 8.8.8.8 then you don't have any outside connection and something is seriously wrong.
Check what '/etc/resolv.conf' says. It should have '# Generated by NetworkManager' there as a first line and then some nameserver lines with their numbers.
You can edit the file and as the top server make:
'nameserver 8.8.8.8'
then save the file and see if DNS works with i.e:
'ping -c 3 www.google.com'
If that works you can alter through the GUI of network-manager by 'right-clicking' on tre network icon and choosing 'edit connections ...' after which:
You can enter the 8.8.8.8 address.
On the machines I have that are installed with 3.8.32 'Retrowave' I have no such problems despite moving them around quite a lot, using various methods of connecting.
So we might have to look deeper at what exactly is ailing your machine. 
Hi Harm,
Thanks for the help, I'll do those tests tonight or tomorrow night and told you the results, is a really strange issue....
Hello again,
Effectively the file resolv.conf done different results,
First in 3.8.30 installed from zero:
Internet goes OK.
Second in default live 3.8.32 with kernel 6.0 in live mode:
Ping 8.8.8.8 seems goes well but no Internet available.
And finally I also tested live 3.8.32 with kernel 5.0 done the same result, ping seems OK but no Internet...
I'm completely lost in this affair...
Pinging 8.8.8.8 means that you do have an internet connection but that the resolving of names corresponding to IP adresses isn't working.
so editing /etc/resolv.conf and adding
nameserver 8.8.8.8
on the first line there, will solve the issue by using Google to resolve the names, after saving that file you'll be able to 'ping www.google.com'
In 3.8.30 DNS is set (by network-manager) to your Access Point 192.168.1.1 which points to the nameserver it has set internally and uses that for all it's clients.
Apparently your other installs do not even see the AP, as a nameserver.
Nice, thanks, tomorrow night I'll try to change resolv.conf file, the strange thing is which has been the changes between releases that makes this issue @Thanatermesis ,any idea?
For somebody that discover elive in first time have an Internet issue would be a reason for not use it and even make bad reviews....
Tomorrow I'll write here results of modifications in the file if I have time to test them.
Greetings!
Modems tend to point to the DNS that the telco sets in the modem when using DHCP combined with some weaknesses network-mamager has.
Albeit that it could also be down to the installer trying to be too clever and reusing existing previous network connections that aren't valid anymore.
Anyway a file '/etc/resov.conf' with omly the line 'nameserver 8.8.8.8' will/should work in all cases.
Looks like we have a serious contender when it comes down to looks and icons:
They make ample use of 'yad' (they don't ... 'yad' conks-out on GTK) and it looks gorgeous (albeit the really cool stuff is in C and Qt).
Even allowing to alter settings in a GUI
So if @Thanatermesis does fall under a bus ..... I'll certainly be having a look there. Albeit it is arch based and I will sorely miss all the hidden little things that he does to make this Elive so cool.
I found that Garuda uses 'BeautyLine' icons which does have a speaker-like icon for the 'cairo-dock' icon:
It can be found on github:
