Out of the box, my EEE PC 1005PE had the same problem. Yours might be
something completely different, but here's the solution I used:
https://wiki.ubuntu.com/HardwareSupport/Machines/Netbooks#Asus%20Eee%20PC%201005PE
In short, the important bit is:
The microphone issue with the 1005HA seems to be present (
https://bugs.launchpad.net/ubuntu/+source/alsa-driver/+bug/449855).
To fix, open a terminal and type 'sudo apt-get install
linux-backports-modules-alsa-karmic-generic'. The mic should then work
after a reboot (at least with the sound recorder app). To get Skype
working, install the pulse audio volume control app 'sudo apt-get
install pavucontrol'. At the Input Devices tab of the app, set the front
left channel to 90% and the front right channel to 10%. Sound Capturing
should now work with skype.
Beyond that, it might just be as simple as not selecting the right device. Right-Click on the sound applet and select Sound Preferences (it might be called somehting similar to that, I only have 10.04 in front of me to test this). In the dialog that pops up, select the "Input" tab and it should list both microphones there. Assuming it does, select the one one want to try and give it a go.
