For a quad gpu setup - none. An MSI 890FXA-GD70 with the cheapest AM3 cpu (Sempron 140) or even an overkill-for-mining Athlon II X2 will cost less than any Intel-based board with 4 full-length pci-e slots. And it will take 4 video cards without extenders (additional cost and waiting time) or 6 with them.
Heck, if it's a higher-end Sandy Bridge, you can probably sell it for more than the MSI + Sempron will cost you

CPUs are speced to undervolt, they do it on their own anyway, when idle. The Athlon X4 640 has an operating voltage range of 0.875V-1.425V. Running it at something like 1V and 1.5GHz will, if anything, probably extend it's lifetime.

It's mostly sold-out or on backorder, with 2+ weeks for delivery. Overclockers UK seems to have it in stock, but they don't deliver to my country . OP may have better luck.

Not all 1000W PSUs are equal... which one exactly did you get?

As for saving power:
 - disable all but one core on the cpu (yes, it will be enough for a dedicated rig)
 - downclock the cpu as low as it will go, then decrease the cpu voltage as low as possible while keeping the cpu stable
 - dowclock the video memory on your cards down to the 150-300MHz range (this can also improve your hashrate)
 - replace the hdd with a usb stick

You should be able to get the cpu down to 10W or less, removing the hdd saves 5-10W (depending on model) and downclocking video memory saves 20-30W per card.

Those are some really shi**y specs. All the power on the 3.3V and 5V rails is basically wasted because most power-hungry components in today's systems (cpu and video cards) get most of their power of the 12V rail. Manufacturers of quality power supplies have adjusted their rail distribution and power ratings accordingly, so an Antec, Corsair, Enermax, etc. PSU will be able to deliver 85%+ of it's rated power on the 12V rail (there are more good PSU manufacturers, I just can't be bothered to list them all ).

Shi**y manufacturers like the one that made this PSU try to scam people with inflated Wattage and cheap components; kinda like with PC speakers . This piece of sh*t would deserve maybe a 500W rating and even then I wouldn't have confidence it could reliably power a 2x5870 rig. 3x5870 is already way out of it's specs.

As for what PSU to actually get - just get any >=1kW model with ~80A or more on the 12V rail. If you had more experience with tweaking your system's power usage you could get away with a good 850W unit.

1. Underclock the memory and overclock the gpu on your 5830's. The gpu should do ~900MHz without increasing voltage, which will yield a power consumption of about 160W and hash rate about 280Mhash/sec, per card.
2. undervolt and underclock your cpu. It should work normally at <1.5GHz and 1V. If you're gonna use linux or windows with the 2.1 sdk, the cpu will idle most of the time anyway, so it should use <10W.
3. if you use linux, 1GB of memory should be enough. That can save you another 5-10W.
4. again, if using linux, you can skip the hard drive and run it from a usb stick, saving another 10w
5. corsair's AX series is a bit overkill for this rig. A TX850W will do just as well and the few % efficiency difference doesn't justify the price difference. The TX costs about $50 less and the lower efficiency will cost you maybe like $2 per month.

A quality 650W psu should be able to supply at least 600 of those Watts on the 12V rail, which is the one that's actually powering pretty much everything in today's systems.
A 5830 has a specified tdp of 175W. Mining doesn't utilize the whole gpu so power consumption during mining should probably be a bit lower. If you downclock the memory to 200-300MHz range you save about 15W per card. So a 5830 at stock gpu and underclocked memory should pull about 150W while mining. Overclocking without overvolting will raise that back to maybe 170W.

So, a quality 650W psu should be able to power 3 5830s, not just 2, with about 100W left over for the rest of the system. Downclock and undervolt your cpu and that should be plenty of W to spare.

The 5830s are a bit better initial $/Mhash, but the 5850s have better W/MHash, which translates into better long-term $/Mhash.
The 5850s will also give you better Mhash/rig, so less overhead costs for remaining components if you plan to build multiple rigs.

Of those reviews, only the techpowerup one lists the power consumption of just the card, the other two list numbers for the whole system. And even those numbers are measured at the socket, so they are 15-20% higher then what the components are pulling from the psu.

Also, those 163W in the techpowerup review are the worst-case scenario, probably running furmark. Mining should use less power as some parts of the gpu are not used at all. And if you downclock the memory (which you should), you save something like 10-20W per card. I'd be surprised if a 6870 at stock gpu clock and downclocked memory uses more than 120W while mining. Overclocking the gpu, without raising the voltage, can push that to maybe 140W. You can reach ~1GHz on the gpu without overvolting.

So the three of them should use some 400W, most of it from the 12V rail. Add max 100W for the rest of the system, so you need a PSU that can output ~40A on the 12V rail. Any quality >=600W PSU should be able to do that, even some 500W might work.

1. not sure about the 4 gpu limit in Windows (I think Windows actually supports up to 8 gpu's, the 4 gpu limit might be just for crossfire), but if you want to use the machine while mining, you can just set the miners on your primary video card (the one your monitor is hooked up to) to lower aggression. That will reduce the gui lag and at low enough aggression even allow you to do some gaming (though that will reduce your hashrate on that video card - some from lower aggression, some from utilizing the gpu for game rendering).
There is one issue though - for mining on the 6990's you will have to run the 2.4 version of AMD SDK. Under Windows, that will utilize 100% of a cpu core per miner (gpu). With two 6990's, that will means 100% utilization of a 4-core cpu. That will increase power consumption and reduce the machine's responsiveness. This doesn't occur under linux.

2. a 6990 under load uses some 300-350W. With overclocking that can reach 400W. Add some 200W for the rest of the system, less if you build a dedicated mining rig. For 3 6990's, you'll need at least a 1200W psu, more if you plan to overclock.

3.1. yes, removing >1kW of heat from a case is a MAJOR issue. Just removing the side panels on the case will not do, you will also have to ensure very good airflow through the case (like several high-airflow case fans). You will still probably have to run the fans on the 6990's at max or near-max rpm, and they are really LOUD. As in, three of them will sound pretty much like a vacuum cleaner.
3.2. Make sure the pci-express slots on your motherboard are spaced far enough apart to allow installation of dual-slot video cards. Even then you will probably have to use spacers between the cards to ensure enough separation for adequate airflow.
3.3. There are motherboards that can accommodate 4 dual-slot video cards. In that case you can theoretically add another 6990, but that will further increase problems with heat, noise and power requirements.

5. don't even think about running a rig with >1kW of power consumption in a room without air conditioning

Total mining n00b here, so please correct me if I'm way off...

If the 50% difficulty jumps continue, what number of BTC's and/or $'s will your brand new rig generate in it's mining lifetime?
Suppose you start it up just after a difficulty jump - in the 10 or so days until the next jump, you will generate X number of BTC's per day for a total of 10*X BTC.
Then the difficulty jumps by 50%, so in the next 10 or so days, you will be generating (2/3)X BTC's per day for a total of 6.67*X BTC. This will then drop to 4.44*X BTC, 2.96*X BTC, 1.97*X BTC, and so on, every 10 days.
Summing it all up, you come to a grand total of 30*X BTC. That's it. That's what your rig will generate in it's entire lifetime. 90% of that will be generated in the first 2 months - after that, you might as well unplug it, because it will no longer cover the cost of electricity.
I think it's worth emphasizing one more time: if the 50% jumps continue every 10 days, your brand new rig will only ever generate 27 times the BTC's it generates on its first day!

So, if you just got a new rig with a pair of 6990's on May 19th, you are probably generating something like 6.4 BTC/day. By mid-end July, you'll have generated some 170 BTC's, at which point it will become uneconomical to operate. Selling those BTC's at current rates will net you about $1100. Subtract electricity costs of $100+ for a total profit of some $1000. Of course, you will also lose something like $500 on selling your rig (you'll have spent about $2000 on it and maybe sell it for $1500 after two months), so that further reduces your net profit.
Now suppose you're just thinking about building your rig; it might take a couple of days to get the parts together and set it up... just in time for the May 27th jump. Your rig will now be good for just 2/3 of those 170 BTC's, so about 113 BTC/$750. After electricity costs and devaluation of your rig, your practically down to break-even!


Now, of course there were a lot of assumptions in this scenario:
- difficulty jumps continue by 50% (when in fact they seem to be getting even worse)
- difficulty jumps continue every 10 days (when it's currently more like 8-9 days)
- BTC/USD remains stable (it could go either way really)

Realistically, the exponential growth of the network's hashing strength will not continue indefinitely. But it doesn't have to - just a couple more 50%/10 days difficulty jumps will mean the currently added rigs will never break even. The fact that the jumps might even exceed 50% and/or be fewer than 10 days apart just makes the problem (exponentially) worse.