These are the instructions I used to get the sound working properly on my Acer Aspire netbook with similar specs. Maybe they could serve as a starting point:
With linux (alsa as modules)
Add one of these as a line in /etc/modprobe.d/sound.conf:
options snd-hda-intel model=acer-aspire
Recommended. Everything works.
options snd-hda-intel model=acer
Everything works, except the internal microphone and turning off the loudspeaker when a headset is plugged in. For some people the internal microphone may work.
options snd-hda-intel model=auto
Both internal and external microphone does not working
Initially, audio doesn't work, except for beeping. The problem may be corrected by editing /usr/share/alsa/alsa.conf and replacing every instance of card 0 with card 1.
As of kernel 3.1, the headphone jack is correctly supported.
From the following pages on wiki.archlinux.org:https://wiki.archlinux.org/index.php/Acer_Aspire_One#With_linux_.28alsa_as_modules.29https://wiki.archlinux.org/index.php/Acer_AO722-BZ454#Audio
For your machine you obviously wouldn't want to add lines referring to Acer, but similar methods might be helpful.