Digital audio connections are generally present when you have multichannel audio capabilities, which most TVs do not (yes there are a few). TVs are generally stereo only, so they only have stereo inputs, and yes you will have to also connect the stereo analog RCA connections if you want to have sound without the receiver turned on. Digital audio will still work to the receiver also, though with both on, you will get sound from both the TV and receiver.
What about HDMI? If that receiver can do switching and your DVD and HD box both have HDMI (or your receiver does upconversion), you could connect both to the receiver and use a single HDMI connection from your receiver to TV.