You should get a 192.168.10.x address on a wired connection also. Is your wired connection on DHCP, i.e., “Obtain an IP address automatically”? If yes, is this happening for all LAN ports?
If both of the above fails, try assign a static IP address to the wired computer. For example, IP address 192.168.1.99, netmask 255.255.255.0, default gateway 192.168.1.1, DNS 192.168.1.1. Will you be able to connect to the Internet with this setting?