External graphics cards works on some systems but not others

Hello my Name is Travis,
This Page was Made in Re-guard To My External Gpu unit, paired with my Hp Pro Book 650 G1
I have Scoured the web looking for realistic help regarding the issues i am having.

My External unit is a "Beast" this is the >Brand< it includes the unit Input Outputs>
1 x Pci Express 16 Input
1 x Hdmi Input
1 x Usb2.0 or 3.0 output
1 x 12V input
1 x 8 Pin standard power input
1 x 6 pin standard output for Power redistribution.

1x HD 6970

My computer is:

OS Name Microsoft Windows 7 Professional
Version 6.1.7601 Service Pack 1 Build 7601
Other OS Description Not Available
OS Manufacturer Microsoft Corporation
System Name 5CG55140W8
System Manufacturer Hewlett-Packard
System Model HP ProBook 650 G1
System Type x64-based PC
Processor Intel(R) Core(TM) i5-4210M CPU @ 2.60GHz, 2601 Mhz, 2 Core(s), 4 Logical Processor(s)
BIOS Version/Date Hewlett-Packard L77 Ver. 01.34, 8/28/2015
SMBIOS Version 2.7
Windows Directory C:\Windows
System Directory C:\Windows\system32
Boot Device \Device\HarddiskVolume1
Locale United States
Hardware Abstraction Layer Version = "6.1.7601.17514"
User Name 5CG55140W8\admin
Time Zone X
Installed Physical Memory (RAM) 8.00 GB
Total Physical Memory 7.45 GB
Available Physical Memory 5.12 GB
Total Virtual Memory 14.9 GB
Available Virtual Memory 12.5 GB
Page File Space 7.45 GB
Page File C:\pagefile.sys

1 x (External Monitor)

Ok, so humbly i say..

I have hooked this "Beast" up to many Laptops, and have had this same issue multiple times. The Issue i am having is very odd, All Items in question are Tested,Working, and yet incompatible. On The Rare occasion That the External Gpu actually preforms an entire "plug and play" everything runs very smoothly. IE; Computer picks up device, they talk, then they have dinner together, exe.. But most often Alot of Computers do not recognize That The GPU even exists in device manager" So i did some lurking in the bios, not a single mpci Option in the entire bios for this machine.. i mean what a crap shoot haha.. i feel like they literally programmed the ports on this machine to limit "freelance tech expansion" .. if so, i guess i can understand why power companies make certain shaped wall plugs for an entire country, just to corner that market???..
and if you could help, I just need a surefire way to TELL this computer to recognize the External Gpu in question. Cant update the bios any further, all drivers have been installed, is it possible that the first time i plugged it in to this pc, it auto installed Drivers? if so how do i access the port directly to tell.. can i override the bios with a modification?, or perhaps a physical modification to the port? Am i able to access some kind of port parameter or modify the data flow for the port? I guess my real question is> Can it be solved, and can it be solved with the human brain? =) Thank you
Also i must reiterate i have set up these external gpu's for some time now and its usually something like 40/60 it actually works(40%).

So we have a functioning laptop "The Hp pro book in question" a functioning Motherboard Extending adapter" "All cords tested for proper current with a voltmeter", All input outputs properly hooked up, this same setup works on many other laptops. All the pins match up, what gives?

And kindly i understand the term "whitelist" but in a world of information, i would think its not very realistic, considering we can just rewrite the code. any information would be greatly appreciated i would love to hear wht you all have to say about this,