# /sbin/ping -c '3' '8.8.8.8'PING 8.8.8.8 (8.8.8.8): 56 data bytes64 bytes from 127.0.0.1: icmp_seq=0 ttl=64 time=0.153 ms64 bytes from 127.0.0.1: icmp_seq=1 ttl=64 time=0.118 ms64 bytes from 127.0.0.1: icmp_seq=2 ttl=64 time=0.142 ms--- 8.8.8.8 ping statistics ---3 packets transmitted, 3 packets received, 0.0% packet lossround-trip min/avg/max/stddev = 0.118/0.138/0.153/0.015 ms
# /sbin/ping -S '192.168.1.1' -c '3' '8.8.8.8'PING 8.8.8.8 (8.8.8.8) from 192.168.1.1: 56 data bytes--- 8.8.8.8 ping statistics ---3 packets transmitted, 0 packets received, 100.0% packet loss
# /sbin/ping -S '79.41.107.165' -c '3' '8.8.8.8'PING 8.8.8.8 (8.8.8.8) from 79.41.107.165: 56 data bytes64 bytes from 127.0.0.1: icmp_seq=0 ttl=64 time=0.156 ms64 bytes from 127.0.0.1: icmp_seq=1 ttl=64 time=0.129 ms64 bytes from 127.0.0.1: icmp_seq=2 ttl=64 time=0.121 ms--- 8.8.8.8 ping statistics ---3 packets transmitted, 3 packets received, 0.0% packet lossround-trip min/avg/max/stddev = 0.121/0.135/0.156/0.015 ms
l@l-schenker:~$ ping 8.8.8.8PING 8.8.8.8 (8.8.8.8) 56(84) bytes of data.^C--- 8.8.8.8 ping statistics ---4 packets transmitted, 0 received, 100% packet loss, time 70ms
ping: cannot resolve www.google.com: Host name lookup failure
Do you actually have a DNS server installed and/or specified on the LAN?
If you can ping by IP address and not by domain name it would indicate that you have a DNS problem