Yes, you can use ribbon risers with video cards
I've often wondered if using those cheap PCI risers with video cards will work--normally, such cards stick out perpendicular to the motherboard, making console-style gaming PCs hard to build. Alan Parekh wanted to go even further, stuffing the spec sheet into a 1U rackmount server enclosure.
And it all works just fine. He's auctioning off the finished machine at eBay.
Small 1U Gaming Computer [Hacked Gadgets]

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The real challenge here isn't electronic -- it's cooling. If he's dealt with that properly, great; if not, this is a very pretty nonfunctional mockup.
I see 6 40mm fans, one blower, and infer the existence of at least one more 40mm fan in the power supply, and probably a little low-profile jobby on the graphics card.
Cooling shouldn't be an issue, you can get multiple Xeons(120+ watts) running 24/7 in a 1U enclosure; but the claim that this is "quiet" has pegged my favorite skepticism eyebrow.
If it's that good why isn't he keeping it?
Yeah, I'll ask the question.
I think cooling will be fine, with all those fans. The problem will be the noise those poky little 30mm fans make...
What Rob Beschizza said. With the whine this thing is going to make, you'll want to rackmount it in a remote data center.
And with only an ATI 3870, that isn't going to be much of a cutting edge gamer. It'll do Far Cry or HL2 on mediocre settings, but forget Crysis or anything else that has come out in the last couple of years... and forget 2560x1600.
Yes on the noise problem with server gear.
I once brought a stock 1U server home to work on for several months while I was doing some server software development (new OS version and some other stuff I couldn't do remotely) and I could not believe how loud it was. In the ISP data center with all the other equipment going, I barely noticed it. But at home... when it was shut in the study with the door closed, I could hear it roaring from across the hall, through another closed door. I ended up SSHing into it from down the hall most of the time so I didn't have to listen to it.
I really doubt you're going to want to game on this.
I've used as much as 4 inches of ribbon cable to connect a PCI video card. It works fine as long as you don't try to run too high a resolution. It certainly handled text mode just fine.
For the record it was a Toshiba Magnia server that I'd upgraded to a smoking 1GHz P3.
The noise, indeed - I have a 2U PA-RISC affair, and it's much like leaving a vacuum cleaner running. Not quite as intense as I imagine a 1U unit with similar cooling requirements would be, but it still lives in my basement.
Of course, I control it via telnet anyway - so unlike the system in the OP, there's no good reason to keep it close.
There appear to be some serious airflow issues: the memory, when installed, will be perpendicular to airflow (blocking the northbridge and cpu). wrt the blower on the cpu: are we looking at its intake end? or its exhaust? either way it does not look well conceived.
Also, as many have of you have pointed out, the combination of those little fans and the blower brings the worst of all worlds from a noise perspective: a low rumbling noise from the blower, and a high-pitch whine from the fans.