This is typical of several dead cards i've seen.
If you're convinced it actually is dead, you might try baking it(re-solder the connections) as a last resort. Don't do this until you've exhausted all other avenues because it may not work, and could make it worse, but could also fix it.
My son has a AMD 7850 that he had for many years. I baked it maybe 6 different times for symptoms just like you're seeing, and it worked many times(over probably 3 years) until we finally just replaced it.