How to set up DNS on the network?

Question

Network administration

Help me please. On one forum they said that the problem is in the DNS settings. But I don't know how and where to set it up.
In a network of 6 computers with 2 cards.
Through one goes the POE Internet through a router. IP is distributed by DHCP. (pictured Network 4). All computers see each other.
Another network (Network 7) has static addresses 192,168,2,x. Here everyone sees each other except for one, on which, in addition to this network, an Unidentified network is also added.

The task is to remove the Unidentified network so that you can work through the second card (without the Internet). Currently, when you turn off the router, one computer ceases to be visible.
ipconfig/all on the problem computer

Thank you

Answer 1

The problem is that the main gateway is not registered on the second card - therefore it does not work.
There are even two of them: 0.0.0.0 and 192.168.2.30 - remove 0.0.0.0

Answer 2

Tell me, please, where to remove?
Here is route delete. Nothing happens
Did route delete 0.0.0.0
It turned out like this. Only one unidentified network left)))