Here's the tutorial in order to get the microphone module working on VAIO VGN-SR46GD laptop.

OS: Linux Mint - Gnome

Important: You need to install build-essential package before beginning this process;

sudo apt-get install build-essential

Download the source file from the web site: Realtek Web site

http://www.realtek.com/downloads/

select the appropriate device (High Definition or AC'97) - for this laptop the device is High Definition

Unzip source code:

tar xfvj alsa-driver-1.0.xx.tar.bz2

Compile and install source code:

cd alsa-driver...

./configure --with-cards=hda-intel

Make

sudo make install

Reboot

After reboot you should have the microphone working, go to sound properties, Input and un-mute it...

Update: Sometimes after installation you might lose all configuration of ALSA, thus losing all input and output devices (happened for me several times), if so use the following instructions to re-configure ALSA. Then you'll have both input and output devices working.

Basically, you need to update Alsa, so:

First add PPA: 

<meta content="text/html; charset=utf-8" http-equiv="content-type" />

sudo add-apt-repository ppa:ubuntu-audio-dev/ppa

Then, apt-get update:

<meta content="text/html; charset=utf-8" http-equiv="content-type" />

sudo apt-get update

Then, Install:

<meta content="text/html; charset=utf-8" http-equiv="content-type" />

sudo apt-get install linux-alsa-driver-modules-$(uname -r)

Then, Reboot. Now you should be Done.

Source: Ubuntu Wiki

That's it, Cheers...