As you've discovered, the H25 does not have an ethernet cable connection, so there's no way to connect an sort of WiFi adapter to it. In a properly configured H25 installation with Single Wire Multiswitch (SWM) dish, the installer should have provided a "Cinema Connection Kit" to bridge the coax-based SWM network to your home network for internet access. The CCK is available in a wireless WiFi version.
That said, there's not a lot you can do with an HD Receiver on the internet. A DVR is required for any OnDemand stuff. What are you hoping to do?