but I'm useless when it comes to routing between different subnets on the same physical network.
I think I tried resetting it a few dozen times but don't get any response.dhclient will not show the IP-address of your router. It will return an IP-address for your "client".
For you client you can assign a fixed IP-address in the same subnet of your router ...
You should "know" the configuration of your router.
If you forgot the configuration of your router you can do a factory reset according to the manual. Sometimes its plugging in a needle and push a switch.