No 5.1 speaker config

What is shown when you Click the "Configure" button for the HDMI? Are you given speaker options?

I can't check mine as I don't have an HDMI plugged in, or any close device I could connect the HDMI to.

Well that explains why there is no 5.1 sound. But, I don't have any info on what is in your video card. You can try the RealTek driver from the link and see if that will install and work. Before you install the driver, set a System Restore point so you can use System Restore to fall back in case it corrupts something.

Ultimately it may take a different video card that does have the wanted 5.1 surround sound.

Others have had this problem and only two appear to have resolved it, but by doing what you've already done, one, two, that is re-installing the graphic driver. Unfortunately I don't have an HDMI cable to experiment on my end.

Edit: In your BIOS, do you have the SPDIF Mode Setting set to HDMI rather than SPDIF output?

There is nothing in the BIOS on my Intel motherboard for any HDMI options.
I have S/PDIF enabled, but that has nothing to do with my HD4850 video card's audio as the HD4850 has it's own sound device built on the Video card.

There are some video cards that require an S/PDIF connection to the PC for HDMI sound, but I don't think any of the HD 4800 series requires this.

Does the driver set you installed for your card have the Dolby encoding drivers? I think the HDMI output will be "stereo" and it's up to the amp to decode the Dolby compression and output 5.1 sound. Your snapshot shows two channels but this doesn't necessarily mean two speakers. HDMI uses two channels for audio. The Dolby compression used on the PC side must match the Dolby decompression capabilities on the amp side.

Edit:
I should have said the sound standard for compression used on the PC side must match the amp. Whether you use Dolby or not really doesn't matter.