Your have no input devices. You keep talking about headphones, but headphones don't allow you to be heard, only to hear. You state the headphones work with your phone, do you mean the pair of headphones that came with your cell phone?
If this is the case, they will not work. You will have to buy a microphone or a headset.
If this is not the case, what type of microphone or headset do you have (USB or analog.) If USB, what brand/model?
After you reply with that information, try connecting your microphone to a different connector (Back/front analog, or different USB port.) Then run through the audio setup from the welcome screen. Below are the instructions for how to setup Skype. Please follow them to the best of your ability.
http/www.skype-lab.com/en/download.html