Logic > take plug from monitor plug to different card/integrated > work? > yes = monitor works.
Logic > Put card that appears to not work in a different computer > work? > no = 99% something is broken.
Does the card have fans? could test for that, does the card have any apparent burnt mark? Does the card smell burnt? Does the card have lights? If yes, does the card lights come on when the computer turn on? Does the bios give out any error code? (things like beeps or led numbers and etc.)
Now what's broken on the card is a different test. Could be the gpu, power on it, circuit, and many numbers of other things.
