Help! DVI+HDMI output in clone mode on HD5670 doesn't work

This is driving me nuts. Please help.

After I installed a new HD5670, I connected it to my AV receiver (Yamaha RX-V765) via HDMI and then another HDMI from the receiver goes to the TV (Panasonic 46PZ80B). Receiver handles audio, TV shows picture, HDMI is set to passthrough in the receiver so that even with the receiver off (standby) the TV shows picture.

Now, when I want to listen to radio I can't use the computer at the same time because the video signal from the receiver to the TV goes to black. Same for all the other audio sources.

So, to solve this, even though it's not the most convenient solution, I thought of using the DVI output from the HD5670 with a DVI-HDMI cable connected directly to the TV. Then set it up as clone display.

This does not work the first time you set it up for some reason (it shows an empty desktop on the second display, as if it's extending the desktop rather than cloning it) but works after a reboot. Yet, if I switch twice from HDMI1 to HDMI2 on my TV, then it doesn't work again (showing the empty desktop again).

Tried playing with the settings many times but unsuccessfully.
Any ideas please?

OS: Windows 7 Pro 64bit, latest ATI catalyst drivers.

PS. The ATI drivers don't distinguish between the two displays in clone mode, there's no primary/secondary, they are just two branches in the same hierarchy (both identified as "1").
I tried disabling (and disconnecting) the HDMI so then the DVI was the only kid in town, then plugging and enabling the HDMI, first setting it as extended with a clear subordinate role (identified as "2") and then setting it as cloned, hoping that internally it would be the second display. And now, DVI shows desktop as normal and the amp shows the little red "HDMI" indication, and sound works, but video doesn't show on the DVI output, and when I switch to HDMI2 on the TV (i.e. the input from the receiver), then the receiver seems to lose the connection to the PC (!). The red "HDMI" indication disappears, and the TV shows a black screen, and audio stops too.
How can it be so difficult?
And worst of all, this scores about -500 WAF points. We had a working system and now that I upgraded everything to have HD-audio, it seems we have nothing!
Help!

I have a suspicion that the biggest difference is actually the OS (32bit vs 64bit, which means different drivers).

Doubt it because each individual connection works the first time I enable it and disable the other one, the problem is that the connection drops if I have both enabled and switch back and forth.

1. it's the same resolution in both cases (1080p) anyway.
2. Correct. it's as if I had a second monitor on the right of the first one.
3. It's either that (in which case it's a card's driver's issue) or that the receiver thinks that because I switched to a different source, I don't want to have the first one active and passing-through to the TV, in which case it's the receiver's issue. Problem is I have tried all the settings in both and I can't find a solution.

It's the same TV btw. What I'm trying to establish is to have the PC video on the TV regardless of the the audio source on the receiver.

The "solution" I've found so far is to have the DVI enabled, and the HDMI disabled, and use the onboard sound (connected to the receiver via SPDIF). Then when and if I want to watch a bluray with HD-audio, I disable the DVI connection, enable the HDMI one and play the movie. After the movie, I switch back. Far from optimal solution though, so I'm still looking for a proper one.

exactly, I was going to reply explaining this.
As I said above, I have a similar setup now and only enable the HDMI output for a movie with hd audio, but i want it on a more permanent and stable basis.