GPU works in 1 computer, but not the one it came in

[Cyannis]

Alright so this is a bit of a bizarre issue but I'll try and make it as clear as possible. The two computer's builds are as follows:

Blue Computer:
CPU: Intel i5-2500k
Heatsink: Generic closed loop liquid cooling, replaced with Thermaltake CLP0556-D
Motherboard: Asus P8P67 LE
PSU: Xion 700W
Original GPU: Radeon 6850 - 1GB - HIS IceQ X Turbo

Red Computer (Modified Gateway FX Series Pre-Built Desktop):
CPU: Intel i7-870
Heatsink: Generic brand air cooler
Motherboard: Generic brand H57H-AM2, unknown model
PSU: 500W FSP450-60EP Power Supply
Original GPU: Nvidia EVGA GTX-760

Liquid cooling gave out on my Blue Computer, so I went and bought an air cooler from Thermaltake. After installing the cooler and turning it on, I got one long beep, followed by three short beeps on the motherboard, then a pause and another long beep. Not sure about the pause-long beep at the end, but one long and three short is apparently a VGA failure. So I replaced the Blue Computer's Radeon with my Red Computer's Nvidia. Works totally fine, I've been using it for several days without issue. I did royally screw up while installing the cooler and dropped it at one point, and thought I may have broken the GPU in the process or scuffed the motherboard in a bad way.

However, when I threw the Radeon into the Red Computer just to see what would happen, it seems to work totally fine in that one. When thrown back into the Blue Computer, I still get the beep code and no video. I would just leave the cards in their new cases, but I'd like to figure out why there's an issue to begin with. Any ideas on what the issue may be and how to resolve it?

TLDR; Replaced heatsink, graphics card suddenly no longer works in that computer but still works in others.

Things I've tried so far:
Trying both of the PCI slots.
Trying both of the 2 six-pin connectors (Granted, the Nvidia needs both+a 2 pin, and the Radeon only needs 1).
Unplugging my new heat sink and plugging the old liquid cooler back in.

Haven't done anything in the BIOS or with the drivers yet.

 

[hang-the-9]

I'd check for a newer BIOS. l have had issues when a video card works in one system but not another one, even though it used to work in that system earlier. Just used it in the system it worked in, never got a fix.