Sudden blackouts without any indication are always difficult to troubleshoot. Happened to me as well once. What i did was take take out GPU and RAM. clean the pc with blower, disconnect and reconnect HDD sata wire and then try again.
Step 1 do is , if you have an onboard graphics card as well? then remove the external GPU and boot thru onboard GPU. this will surely diagnose if GPU is the culprit or not
if still no display then again remove GPU and RAM, clean their connecting pins with soft rubber (pencil rubber) wipe off the rub with very soft lint free cloth. then again try to boot (see this video on cleaning pins:
How To clean contacts of pci/video cards - YouTube)
If your PC still does not boot then you need to check MB, HDD, PSU, GPU to find the culprit.