Huh...
That's unfortunate. There is just very little, almost nothing in fact, to go on here.
I mean, my instinct is that the card may be faulty. Whether it's been a long time coming or something happened when you changed your GPU/installed your new GPU's driver, I do not know. Nor am I implying you did something wrong.
Thing is, besides your monitor's built in speakers working fine, there isn't any ways to test a sound card the same way you could test, say, a GPU. At least, not to my knowledge. Your motherboard's on-board is shot from what I understand and you don't have speakers or other devices to test out.
Have you tried removing the sound card's drivers completely and reinstalling them?
If you already have done so, then I'm running out of ideas.