What I'm guessing is that you need to run SPDIF to the graphics card/HDMI port. My old GeForce 9500 needed it, but I never bothered hooking it up before I got a newer card that didn't need it.
It's a weird looking connector, I think you need a special cable for it.
Of course, Mete's solution is much more likely if it's a newer computer, or if the HDMI is through an integrated (built into the motherboard) chip.
EDIT:
Can anyone help me look for a computer? I'd like to keep it as far below $600 as possible, absolutely not going over. The only part that matters much is the processor, I'd prefer not to go below an i5 3470. My only other requirement is that I be able to put in a graphics card - I found one computer that would have been perfect, but for having half-length PCIe slots, which my card won't fit in. (Nor, apparently, will anything worth using.)
I've looked at Newegg and TigerDirect, and every computer in my range that I've looked at has either had too slender a case for my card or the wrong ports entirely.
I'm going for pre-built because I've had bad luck with putting stuff together before. I know the advantages of buying components, this is my choice. I might be persuaded if there aren't any computers that fit my needs, but I'd prefer to keep my own mistakes from being a risk factor until I put in my graphics card.
So, recap: any prebuilt machine under $600 with an i5 3470 (3.2 ghz) and a regular PCIe x16 slot.
EDIT 2: woah wait hold up, anyone see any glaring issues with
this?