Are you sure that this laptop has a build in microphone? or are you using a external microphone?
in either case the most likely problem is that the skype sound settings on the input are wrong.
open skype, tools, options, then the audio settings page.
On the microphone, try all the possible options offered and see if it detects your voice, you can also try calling the skype test number / echo123.
When you see the volume bar light up green like this as you speak or tap the microphone its working.
If you are using a external microphone, are you sure you have it on the right slot? Try the other plugs on the laptop and then go over the options again and see if you get sound.
You should also check from volume control that the microphone is not muted.
To check that open up start -> control panel -> sounds -> recording -> select the microphone and click properties -> check the levels tap and make sure its not muted and its turned up to full volume.
also some microphones have a on off switch on the wire, make sure its turned on.
By now you should be able to talk on skype.
Let me know if you need further assistance.