Use Airport Express as a WIFI extender on non-Apple

Check what wireless networks are available. It is possible your Airport Express is broadcasting a secondary wifi network. If so, try connecting to that network and searching for base stations again.

As a last resort, you can perform a reset. Try a configuration reset first (hold the reset button down with the tip of a pencil for a few seconds, until the led flashes rapidly). If that doesn't work, try a factory reset, by unplugging and replugging it, holding down the reset button.

The DHCP works fine for the airport.

If you use ethernet and a static IP address, then you'll have to choose an IP address outside of the DHCP lease range otherwise you can get IP address conflicts.

For example, if your DHCP range is set to 192.168.0.10 through 192.168.0.20 then you can use the IP address ranges 192.168.0.1 - 192.168.0.9 and 192.168.0.21 - 192.168.0.253 for statically assigned IP address.

Hope this helps