GPU only working in a specific case.

Jul 22, 2018
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Recently my PC started rebooting while gaming. The initial Google search brought up possible problems with the PSU. However, meanwhile I got a whole system and a new case - only the 970 is still left from the old system. With the new system i can't even launch a game from the main menu. Regardless the game I get a black screen and have to reboot. So I thought that the GPU might be the problem after all.
The GPU, however, is working perfectly fine in my wife's system, which is is my old system - the exact system the 970 did not work with before only in a different case. An older GPU (GTX 660 which is now installed in my wife's system) works perfectly fine in both my new and old system. I tried switching monitors, using a diffetent socket but nothing works. Has anyone any idea what might be the problem here?
 
Jul 22, 2018
4
0
10
All drivers are up to date and freshly installed. Full Specs:

The GPU is an Asus GTX 970 Strix DirectCUII

New System:
Asus B360 Strix Gaming-F Motherboard
Intel i5 8400
16GB (2x8) G.Skill Trident Z RGB DDR4-2666
Seasonic Focus 550W PSU
500GB Samsung 860 Evo
1 TB Western Digital HDD
Fractal Design Meshify C

The OLD System (in which the 970 works again but did not before):
Asus P8Z77-V LX2
Intel i5 3470
8GB (2x4) Corsair LP DDR3-1333
beQuiet! Pure Power L8 530W
128GB Samsung 840 Evo
500 GB Samsung 850 Evo
SilverStone RL7 Redline