First thing: Do the headphones work in a different USB port? If so, you may have solved your problem in record time -- and it's time to figure out why that USB port is bad, but that's another story.
If they still don't work: Do the headphones work in a different system? Doesn't take a genius to figure out that would point to bad headphones.
If neither of those solve your problem ... if I had to guess, easiest thing would be a driver conflict/outdated driver. What OS are you using, and did you install either the OS, any components, or the headphones recently? If yes (or if you're using Windows 7), try searching for any driver updates for the motherboard, headphones, probably the the video card just for good measure. See if installing the latest ones helps.
One other relatively simple thing to check is whether the wires from the USB port are making good contact with the pins on the board. It's probably worth taking a look in your case to see if they're loose, plugged in one pin off, or anything of that nature. Occasionally, you may also run into case wires whose connectors have worn out and the pins inside are slightly bent, so they make only loose/intermittent contact. Kind of like what happens to old original NES systems where you have to blow on the games and they only work for a few minutes. I had that happen to me recently with the pins from the power switch to the case, and it was a tremendous pain in the ass to troubleshoot. Haven't heard of it happening with the USB connectors, but there's a first time for everything.