Yeah, I'm not seeing any info on the combined amps for the +12v rails. If I had to guess I would have thought it would work but the brand isn't very good and the wattage may be highly overstated. It certainly does sound like the card isn't getting enough power under load from what you describe.
If the card has a factory overclock you may want to try setting it down to reference speeds/voltage(675mhz/1.025v) with a program like Afterburner. http://downloads.guru3d.com/Afterburner-2.1.0_d2562.htm...
It may help the card work for now but I would really replace that power supply with something from a more respectable brand.
Thermaltake also is not a very good brand. They do have some decent units but they are high end and rather expensive. I believe the one you are looking at doesn't even have active PFC which is the first thing to look for in a PSU. Don't get caught up in the listed wattage of the PSUs. They are often outright lies. I would recommend something like this; http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Antec is one of the best brands and their units are highly reliable. It is rated for continuous usage rather than peak like most and has 40a/480w on the +12v rail which is more than enough for your system.
if you want something cheaper from thermaltake hardware secrets reviewed the litepower and it actually got a good review. TR2's are known for not producing their rated power and ripple going out of spec when under heavy load, that being said your current setup shouldnt even be pulling over 50% of the psu's rated power so it should be ok. There are also many variations of the tr2, some are completely different designs. http://www.anandtech.com/show/2670/9 http://www.hardwaresecrets.com/article/Thermaltake-TR2-... 2 reviews of different models from the series, notice the very different conclusions
(edit) Your setup: (/edit)
Minimum PSU Wattage: 346 W
Recommended PSU Wattage: 396 W
This is with 30% capacitor aging which is enough to run it 24/7 for a year and assuming you have 3 92mm fans and 3 extra usb devices
The other reason its an issue for you is that the minimum 12v rail power is 38A for that card. I know you said you were running both rails into it but it appears its not working like intended. Better to go with a single rail instead... simpler math.
future proofing him a tad but not too much that he goes and blows his wad on a 1200w one. If he decides in say 6 months to upgrade his video card he will be able to get pretty much anything on the market still. Of course Id be a tad leery myself of putting a 580 on this motherboard but hey its his system.
 also dont know what case hes got this in... if its a htpc or shuttle type case he might not be able to get a bigger card but thats an issue for him to solve. I mean hes using basically 350-400w now, might as well go up a level or two so he doesnt have to keep buying psus every time he wants to add something to his system.
The card draws 127 watts .... should certainly be no great shakes for any 650 watter. Easy enough to tell. Run OCCT's GPU test monitoring both voltages and temperature. Should immediately determine which is the cause of your problem.