Try 192.168.1.2 Or 192.168.0.2

Don't forget to set your DNS server IPs and subnet mask. Just use the Subnet you currently have (command prompt: ipconfig /all). Your gateway should be 192.168.1.1. Any Internet DNS IP should work for internet access. Just because you are restricted to that 1 DHCP address doesn't necessarily mean you can't physically assign yourself another. If that router model is locking your particular LAN port to that specific IP than you may need to change ports on the Router/Switch.