Sony DVD through ONKYO TX SR608 reciever to Sharp tv issue
Well, the Onkyo has HDMI switching, so unless there's an issue with the receiver itself, that's not the problem. I see it has labels for all the different HDMI inputs, and I assume you connected the Sony to the appropriate one, so that variable is out of the mix.
Some video devices "default" to a particular output, whether or not your Sony does I cannot say. But for example, since your DVD can display composite ( RCA ), S-video, as well as HDMI, it's possible it defaults to say, composite video. If that's the case, then you'd get nothing hooking it up by S-video or HDMI. That's highly unlikely though......especially if the DVD player isn't new, in other words, you've been watching on another TV.
Conversely, some receivers have inputs "deactivated", and one must manually activate a particular input. My older Denon receivers and Krell pre-amp have that, and go so far as to be able to assign ( de/activate ) audio inputs as either digital ( optical or composite ) or analog composite.
Check both the receiver and the DVD players' manuals for any defaulted audio/video paths, and if they have user selected in/outputs for them. It make take some time going back and forth, as manufacturers ( manual writers to be specific ), seem to take great pleasure in having the end user going all over creation in them in order to get things in harmony....