Thank you to everyone who has tried to help.
I bought a new HDMI 1.3 rated cable only 4 feet long, but that did not change anything except my checking account balance.
I have run a couple of experiments using my 1920x1080 computer monitor in place of the projector. The monitor has HDMI, DVI & VGA inputs.
I first connected the monitor directly to the DirecTV receiver using a HDMI-to DVI-cable using the DVI input and that worked perfectly.
I then tried using that same cable from the receiver's HDMI output to the DVI input of the HD Fury and then into the VGA input of the monitor. That resulted in no picture. At least when I used that setup with the projector, I at least got a couple minutes of garbled flickering image before it went to a black screen. Yes, I did select VGA input on the monitor (after forgetting to at first). The monitor just give a mesage saying "no signal".
Now one thing I did discover is that the DirecTV receiver automatically chooses the highest video input the TV will accept, so if the HD Fury can accept 1080p then that is what is sending and there is no manual limit setting on the receiver. If so, then the projector is being sent a 1080p signal and it can't handle that. The only thing that makes me question that theory is that the monitor should have been able to receive a 1080p signal from the HD Fury but didn't.
I don't think I have any other hdmi devices, but my DVD does have a dvi output, although it will allow an analog signal out on the dvi, so that is how I have it set.
Any other suggestions?