Have you tried another set of earbuds? Those things see tons of "abuse" and the wires can be fragile and break. When the headphones are plugged in, if they have a microphone, the internal microphone on the phone is disabled so it makes sense that if the earbuds have failed the other person can't hear you.
If another set of earbuds doesn't work, then it stands to reason that the headphone jack in the phone is causing the problem.
If you need additional help or have more questions or details to share, please join the site so you can reply in this thread. See
this link for instructions on how to join Android Central.