Here is a list of things that can help when trying to eliminate moises picked up by your microphone.
  1. The first thing to check is that the latest drivers for your sound card are installed. Drivers can fix similar issue like background noises.

  2. Be sure that you are using an headset and not speakers to play your sounds. The microphone can pick up the sound from the speakers which can create noises and bad echo.

  3. Some noises are reported to be caused by computer parts such as case fans, power supply, video card fan. It is hard to determine for sure if it's the cause and there is no real solution.

  4. Some poeple get a "hummming" sound when they speak, that is often reported with unboard sound card, be sure the latest drivers are installed. Some humming sound can be caused by bad power but it is pretty rare and can not be confirmed except by trying another power supply. Adding a PCI sound card can fix this issue but can not be verify unless a new card is installed to your computer.

  5. in some cases it can simply be a bad microphone or microphone cable. Try moving/shaking the microphone cable when speaking and see if it amplify your noises. Of course if you have another microphone avaible for testing it is the best way to determine if it is the cause of your noises.