What are you watching? What are you using as a source for the programming in question? HD or SD? If you're using a cable box, satellite receiver, etc., and particularly if you're watching HD, you'll need to use the caption decoder in that device - there's still (last I knew) no agreed upon way to transport closed captioning data over HDMI other than having it composited in by the receiving device.
I have the DirecTV R-15 DVR (Not the HD receiver, I just got the TV today, so I haven't upgraded the receiver yet) ... and the Onkyo TX-SR605 is the audio receiver. I have not tried to by pass the receiver ... but I didn't have to so that on my standard TV.
You need to continue to use whatever method you had the STB connected to the TV for now instead of HDMI until you can upgrade to an HD STB. As noted, the HD STB will do the CC's internally and pass them as part of the video to the TV when they are enabled, you can't pass the CC data via HDMI and have the TV read it and display them.
As far as I can tell, you can pass closed captions through to the TV (as opposed to "burning them into the image" at the set-top box) only through a 480i analog connection (composite, component or S-video).