1.what is your host system if you are using only the live CD.
2.Where you are using this live CD is it on a virtual box or just trying on main partition.
3.How this machine is connected to internet(using router or directly wired connection from the service provider.
4.Is there any MAC address bind to the machine by the service provider). If this machine is bind with the mac address by the service provider you will not be able to use the connection from any other physical or virtual machine.
I have changed the network card. It´s the same model, but another card.
Then I delete the configuration and create a new configuration.
After this, the command ifconfig shows, that the card is up and was configured correct.
The MAC-address is now the correct address:
The ping-command works fine and I can connect to the internet.