Fix: You must physically relocate the microphone and move it away from the speakers...or move the speakers away OR mute the microphone output, so that no feedback loop is established.
This means you need to go into your volume control program and MUTE the microphone. This means you may not hear your own voice when you speak into it, but it's still recording, just not outputting the sound to the speakers. (if you don't believe me, then mute the microphone, start Sound Recorder and record something.)
You may be able to reduce the volume of the microphone output, but that isn't guaranteed to work. Additionally, you can plug headphones into the computer, instead of speakers. This eliminates the problem as well.
Depending on what model your Sound Card is, you may be able to enable "Noise Cancellation", which will put a stop to the screeching. This is common in most decent OEM soundcard brands like Realtek