HDCP only from DVI, audio only from HDMI, weird

Are you using your terminology correctly?

Standard DVI-HDMI cables chop off the audio output from what I've seen, using them on a graphics card that otherwise outputs audio via DVI. This makes sense though, because DVI doesn't't have audio included in the cable specs.
However, for cards that use special dongle adapters, I think they use a dual-link cable, but passing passing video on one link, and audio seperately. if you look at standard DVI-HDMI cables, they are always single-link only for the pins on the DVI side.
If you look at HDMI specs, you'll notice multiple data-channels. I think one is used for audio and they aren't merged, so it's easy to see that the special dongles wire the pins to pass both links to the appropriate HDMI pins. I think they wrote HDMI to be at least partial backwards compatible with DVI.
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So basically, you have a standard DVI-HDMI cable, yet a non-standard DVI interface trying to pass audio.

That's probably why. You need the special dongle though I'm not familiar with nVidia cards for this.

Your NVIDIA card apparently only supports both video and audio over it's HDMI output connection and does not support an internal audio connection to support audio output over it's DVI connection. ATI cards with audio over DVI output use a special dongle as indicated above.
With HDMI the video and audio are multiplexed over the signal connections so no special cables are required a regular HDMI-HDMI cable will work fine.
Your second configuration should work fine.
What driver release from Nvidia are you using with OS release?
What resolution are you sending over the HDMI interface?

Take their response with a grain of salt.. I've dealt with the likes of support for Gateway, Dell, Compaq (in the day) and HP. Back in my younger years I did IT admin and support for a University college. But our agreement was with student laptops too. Let's just say you get much better support with a business contract from a computer company. In fact, consumer computer support blows to be honest... So we were forced to do the less help consumer support lines for things like warranties and such. We couldn't use our "business support" options on a consumer laptop.

In my dealings, Let's just say if you didn't escalate this high enough you could be getting inaccurate info (it can actually be tricky to know when it's been escalated to the point where you should get a proper answer from someone knowledgeable). In fact talking on a forum will probably get you farther. There was a generation of nVidia cards *7000, maybe 8000* that had HDCP as an option and many didn't, but now they all do because the demand is there. Also aren't the lowerend 9000 series nVidia video only?
Yes Jeff the 1080p is really suspicious. 720p is certainly a mainstay in HD. You probably want to escalate the call with them, especially if it's branded by HP.

I think the HP rep has absolutely no idea what he is talking about.
I am surprised that MC is giving you the message about HDCP over the HDMI connector.
However since the card apparently does not support audio over HDMI then I suggest that you use the DVI out and the DVI-HDMI converter cable and then connect the audio out from your system to a HDMI port on your TV that also supports Red and White stereo inputs. (check your TV user manual for details there is probably only one HDMI input that supports either HDMI or R&W audio input)
You can get a minipin computer audio output connector to R&W audio cable connector at Radio Shack.

With many HDTVs that have one HDMI port that supports either HDMI audio or R&W audio there is also a setting in the TV to tell it which to use since it does not automatically detect the R&W signal and switch to it.
Of course the card supports 720p I have never seen an NVIDIA card that does not in the last 4 years.

Not all Hi Def signals require HDCP only those from some sources and those from HD or BR disks. Since VGA and Component are broadcasst and not handshaking protocols they can not support HDCP and work since none of the studios have implemented the flag that requires that HD content be downscaled to SD resolution for other then digital output that supports HDCP.