|Does the thermaltake power supply read error codes from the motherboard or some such and shut down while the cheap power supply just dumbly supply power?|
No quite but the chip-set on the motherboard does control the power supply and will shut it down if it detects a fault condition like a short circuit. Cheap power supplies may not have all the control circuits necessary to allow it to respond to the signal from the motherboard.
I would say there is nothing wrong with the power supply but there is something wrong with the motherboard that the Power On Self Test is detecting and it is shutting down the power supply to prevent further damage.
If you continue to use the cheap power supply you may eventually damage something beyond redemption. I would find out what is causing the shut down which could be near impossible as you already done the standard trouble shooting procedure by stripping out everything that is not necessary.
The only other thing you can do is remove the remaining hard disk. At least you should still get a BIOS screen and a prompt to insert system disk. If you get that far and no shut down then you have found the problem. If you have more than one memory module try removing one then the other and see if that makes any difference.