Most evident step - check if the music is turned off in settings.

Then go to:
C:\Program Files (x86)\Steam\steamapps\common\TheImpossibleGame\res
(or where is your The Impossible Game installed?)
and find there some .ogg files. Copy them to some directory for easy access. We will use them in next steps.

I personally use http://online-audio-converter.com/
Press "Open files" button and select all your ogg files that you copied in previous step

Wait until the upload is finished

Press "Convert button", wait a little bit and download converted files.

You'll got a zip archive with some files. Extract it to any folder.

Now you have a folder with some mp3 files

Rename all .mp3 files to .ogg, like this (Always press "yes" button)

At the end it should look like this:

Copy .ogg files, that you've got in previous step back into res folder
(C:\Program Files (x86)\Steam\steamapps\common\TheImpossibleGame\res or something)
Tick the box and choose "Replace"
After that, the game should work! Comment if this doesn't, I'll try to help you. If you removed .ogg files, you always can follow this guide