Can the PSU not add power to the video card and what to do?

Question

Iron

In general, an external PCIe video card began to turn off by itself, even without load. The image on the monitor disappears and previously only turning off the power and turning on the PC again helped. I reset the BIOS and it's better. Now the screen goes blank less often and only for a short time. But when you reboot, the initial BIOS screen is not visible, the image appears only when you select the OS (I have 2 Windows).
Actually prehistory: a week ago, the PSU burned out from overheating. It was Deep Cool. Worked great, had no problems with it. Went to the store and without thinking twice took some Cougar. On the box is an inscription that has a bronze certificate. Came home, installed it and ran it. After half an hour, the screen turned off during a conversation on Google Hangouts and did not turn on again until I restarted the PC.
Question: what to do and how to be?