From my experience, if a component does not work, the problem is a) hardware incompatibility, or b) software issues (also incompatibility) . I agree with the cooling fan capacity test, although many video cards run at such high temperature levels that they have their own integrated cooling fan.
Based on the responses thus far, I wonder if the software driver (that allows the video card to function correctly) is not correct for both your video card and your operating system? The correct or current drivers can usually be downloaded from the PC OEM or video card manufacturer's website. I don't believe that you have a BIOS configuration issue, although that does happen.
The operating system loads the hardware and software during the boot up phase which explains why you are seeing a black screen with a blinking cursor. The O/S cannot load the correct driver (or has an issue) and may stop during the POST (Power-On-Self-Test)
"When power is turned on, POST (Power-On Self-Test) is the diagnostic testing sequence that a computer's basic input/output system (or "start up program") runs to determine if the computer keyboard, random access memory, disk drives, and other hardware are working correctly."
