It depends on which sound card you have, and on potentially plenty of other details. Precise already which sound card you have, if you know it.
You need to provide more details as well. Are you able to play sound? Is the problem only about recording? What do you mean by "failing"? Do you have an error, or simply the recorder is not "hearing" you?
In this last case, you might want to check your audio recording options, and check if the correct source (microphone, normally) is selected, as well as the volume of it. (You can find a tutorial about it at this link)
Edit: Your usb headphone is probably installing its own sound driver, and is taking place of the regular sound card for recording. There is probably only one channel for it, so it works good. Check what I recommended you in the above lines, make sure that your sound card is selected as the default recording device (in sound options), and check that the microphone is selected as the recording channel to use, in the mixer.
Edit2: If settings are correct, I don't have much more to propose besides trying microphone on another computer, and trying another microphone on the computer where there is a problem, to be sure where is the issue.