It looks like the DNS access is failing, you are only getting as far as the router, but the router cannot communicate with the ISP modem. It will, of course, under those circumstanxces, still be able to ping the other computers on the Lan. Try, in the first instance, this. Find the Network adapter in the device manager and disable it. Now reset the ISP Modem (Just a quick reset - on/off) and the router ditto. Re-enable the Network adapter, log off and on again and see if the connection is established.
If not,try a reset, like this:
Open a Command Prompt (Run as Administrator)
Type, in turn, the following commands, and "enter" after each.
1. To reset the WINSOCK entries to the defaults:
netsh winsock reset catalog
2. To reset IPv4 TCP/IP stack to the defaults.
netsh int ipv4 reset reset.log
3. To Reset the IPv6 TCP/IP stack to installation to the defaults.
netsh int ipv6 reset reset.log
Reboot the and see if you have a connection.