Problem with custom-built gaming computer

I did indeed move the power supply over.
I'm thinking there's something wrong with the connections/slots in the internals of the computer, but that doesn't really explain why normal computer functions work.

Then I would say that the new case likely has far poorer air circulation for whatever reason, and you're triggering a thermal cutoff. Some component is getting dangerously hot, and so in an effort to try and prevent the equivalent of a meltdown, it shuts the computer off to let some of the heat dissipate.

I agree this sounds like something is overheating. Download SpeedFan and check. If the cores are under 50 degrees C, you're OK, if over 65 you have a problem, in between bears watching. Make sure the fan on the CPU is spinning when powered on. Make sure the air ducts aren't blocked. I use extra fans that go into the expansion slots and are powered from the mobo - they cost around $10 and help circulation.

Good luck.

Ok, so I downloaded SpeedFan and it is a really nice tool.

Here is what it looks like when no programs are running on the computer:
GPU: 57C (fire symbol)
System: 94C (fire symbol)
CPU: 51C (fire symbol)
AUX: 26C (blue arrow down)
Temp: 94C (fire symbol)
HD0: 26C (blue arrow down)
HD1: 25C (blue arrow down)
Core 0: 47C (green check)
Core 1: 42C (green check)

HOWEVER...

When I started playing Starcraft 2, I checked back on these temperatures and pretty much everything went up, particularly both cores, which skyrocket to about the 70s-80s C.

So this is definitely an overheat problem.. any ideas on how to fix it?

I'm hoping this is the only problem with the computer, because the 5 minutes I played before the computer shut down were great.

Every computer, desktop or laptop will accumulate dust which acts like a blanket to keep heat in. You need to remove the covers and carefully remove the dust at least once a year. Be very careful to ground yourself first and try to avoid touching components other than fans and the CPU's heat sink. Be sure to blow the dust out of the air intakes and in between the fins on the heat sink. Remove the dust bunnies first, then use compressed gas. Also add the exhaust fan I mentioned earlier. When your temps get over 80 degrees, you're in serious danger of damaging components. I hope that hasn't already happened, but those temps you reported are alarming.

Good luck.

CPU heatsink fan ? If not, I'd check it carefully to ensure the CPU HS fan is running and the heatsink is securely attached. I'd check the case fans too.

Personally, I'd opt for a high efficiency CPU HS Fan where you can improve the CPU cooling significantly with an aftermarket unit. Check http://www/frostytech.com as they have reviews on a majority of the aftermarket CPU HS Fans units.

VAPCMD