Install Sony Firmware Extension Parser and Sony Vaio Control Center. Then modify registry: HKLM\System\CurrentControlSet\Control\Class\4d36e968-e...\0000 → Add KMD_EnableBrightnessInterface2 = 0.
Set Realtek HD Audio as default playback device. If still silent, try installing Microsoft UAA Bus Driver for High Definition Audio before the Realtek driver.
Many users have uploaded original Sony driver discs to the Internet Archive. Search for:
"Sony Vaio VGN-FW" drivers OR "PCG-61A11U restoration disc"