Win 2012 R2 local LAN no internet connection

wrong gateway, or DNS not forwarding the request.
try a ping www.google.com
then ping 8.8.8.8
if both fail, it's the gateway, if the first fail, it's the DNS

is the gateway setting correct?
can they ping the gateway?
how far does traceroute 8.8.8.8 go?

Maybe I was not clear with my question.
I use two NICs, one for the internet gateway and the other for the internal LAN.
internet gateway is ok.
I set up a DNS 192.168.20.1, this is also the fix IP from the Internal LAN NIC.

ping www.google.com
then ping 8.8.8.8 both OK

traceroute 8.8.8.8 traceroute?

did you do the ping from the server or from the PC.
the test needed to be done on the PC.
But since you are dual headed the problem is most likely a routing issue on the server.

OK, now I tried on the PC-Client. It's surely a routing problem. Do I need a NAT?

Thanks

Is there really a need to be dual homed (as you did)?
The benefit are limited, and the configuration problems it bring on the server are not worth the pain.
Being dual homed was recommended for W2000-2003, but from 2008 onward, the reverse is recommended.
And if you need RRAS for VPN, it now works on single adapter systems

How should I do that better?

Maybe now I understand. Only one NIC? And the DHCP Range in the range of the router?
example: router 192.168.1.1, DHCP-Range 192.168.1.50 -150?

Yes that's it.
But if you plan to use vpn, it would be best to adapt the range of the router to someting less used (like you did initially).
Note that you can also still use both network card and plug them in parallel to the switch to speed up file transfer (Server 2012 as a switch independent teaming mode).

Also note that you need to disable the DHCP on the router (often easy)
Or configure the router DHCP with the options needed by the client of the server: the domain and dns option. Usually those options are not available in of the shelve and ISP modem/routers.
(Edited for clarification)

Thanks, all is now clear for me