Too much for my PSU?

Hey guys,

The other day I upgraded from an AMD Athlon II X4 640 on an ASUS M4N98TD-EVO to an Intel i7-3820 on an ASUS Rampage IV Extreme. I also added two SATA hard drives.

I was running my system with my old setup:

Athlon II X4 640
M4N98TD-EVO
Gainward Geforce GTX 570 Phantom
Galaxy Geforce 8600GT
4x2GB Corsair 1600MHz RAM
4x SATA HDDs
7x Prolimatech Blue Vortex 140mm Fans
4x 120mm Blue LED Fans

(I mentioned the fans basically because there are a lot, and I'm sure they are drawing a bit of power)

On my Vantec ION2+ 600w PSU. Everything ran fine, I wasn't overclocking at that point, mainly because I was expecting the upgrade and pretty much couldn't be bothered.

Anyway when I upgraded to:

i7-3820
Rampage IV Extreme
Gainward Geforce GTX 570 Phantom
Galaxy Geforce 8600GT
4x2GB Corsair 1600MHz RAM
6x SATA HDDs
7x Prolimatech Blue Vortex 140mm Fans
4x 120mm Blue LED Fans

(Again, I mentioned the fans basically because there are a lot, and I'm sure they are drawing a bit of power)

After reinstalling windows my PC began freezing randomly. Usually about 20 minutes of use the display would freeze, any sound playing would cut out, and the PC would be completely unresponsive. I basically had to reboot every time.
I did a bit of research and when that happens it's ether your CPU, RAM or my hardware is too much for my PSU.
So I did a bit of testing. First I reseated all my RAM, but the freezing continued. I tried each stick of RAM individually and it still continued. So it doesn't seem to be the RAM. After that I tried reseating the CPU, but the problem still continued. So at that point I assumed it was my PSU. So I removed my 570 and I am just using my 8600. I've had my PC running for a few hours now and nothing has gone wrong.

So have I found the problem? Is all my hardware too much for my PSU?
If it is what PSU would you guys recommend I get if I am planning on overclocking and maybe expanding my storage? If I haven't found the issue what else might it actually be, considering my PC is running fine without the 570?

Thanks guys, I hope I've given enough info to figure this one out.

I guess I should have mentioned I've used that calculator and it does seem like I'm stressing my PSU a bit. There's really no headroom at all. I guess this calls for a new PSU then?

Yep, I tested with Prime95 and it did shut off pretty much straight away. Looks like a definite case of a shoddy PSU. I'll be getting some form of 800w+, preferably Corsair. But for now I'm using dual PSUs. No issues so far.
Thanks guys!

I know, I plan on expanding to SLI anyway, so I'm futureproofing.