Go to the volume bar on the bottom right of your computer, right click, recording devices, cycle through the ones that are there and are shown to be working (as in, they are picked up by your computer): try speaking then, and seeing if you get a response out of it.
Skype has a tendency to be a complete d**k with your recording and playback devices. It never holds settings well, so when you installed your new GPU, it might've reset the settings that it had. I realize you've checked in Skype, but try checking in your Volume => Recording devices settings to see if your mic there is working and then cross reference that to the mic that Skype shows it's attempting to use.