Two other possibilities include firmware issues w/ cable box & HDMI handshake issues between cable box & Onkyo receiver. You also quite possibly have a defective receiver. (Are you still under warranty, btw?) I'd put power supply on the very bottom compared to these, since the other possiblities are not at all uncommon if you do some reading. Try over at AVS forum for more discussion on this stuff. Sorry I don't have any specific experience with your exact models to give you quick fix.
Keep in mind only the expanded Blu Ray audio will benefit from the surround sound processing on the receiver via HDMI. Your cable box (which brand/model, btw?) only outputs DD5.1 and none of the wideband audio codecs, so you could still get surround sound by running a separate digital optical out into the Onkyo, at least until you find a solution which permits you to utilize only HDMI connections. So basically, the HDTV acts as a monitor like it should.
I don't own a PS3, so I dont' know if you could also split the audio/video like you can with a typical Cable box. Many folks don't run all HDMI to the receivers, FWIW.
My components are very straight forward, but my knowledge with A/V is lacking:
Sony XBR / Onkyo TX-SR674 / Cable box / PS3-Blueray
1st quality HDMI cables from cable box and ps3 to HDMI IN-1 and 2 on the receiver. HDMI out from receiver to XBR.
So when I select which component (cable or ps3) I choose Video IN1 or Video IN2 on the receiver. The list of problems I then experience is ridiculous, indicating that I don't know what I am doing.
Cable: receiver is VERY slow to process the request and often never finds the connection a tall. When it does, it occasionally connects the video but will not give me the surround sound. Simply switching channels causes the system to go searching for 8-10 seconds. Sometimes in connects, often not.
PS3/Blueray: receiver has no problem recognizing the request for IN2 switching, but cannot hold the signal. TV screen flashes in and out and will often go black for minutes at a time.
I have read a few forum's suggesting power supply can be the root of many unknowns. I currently have the system set up to power on through the cable box. (onkyo power in back of box, tv power to back of Onkyo) The PS3 is powered independently.
I have unplugged the entire Onkyo surround system and watch cable and Blueray through direct link to the tv. Since the surround is such an enjoyable piece of the HD sports and movie experience, I thought I would start here. - Any comments? (other than read the manual, I have and just cannot seem to get there)