O artigo de solução de problemas do Skype na Wiki Help do Ubuntu solucionou o problema de maneira muito clara. Eu usei as instruções "versões antigas do Ubuntu".
Skype has been known to mess up the mixer settings. So disable the automatic configuration of the mixer controls in Skype: right-click with your mouse on the Skype icon in the system tray - Options - Sound Devices - remove the tick at: Allow Skype to automatically adjust my mixer levels. Click Apply. Then close Skype (right-click with your mouse on the Skype icon - Quit).
Then use Synaptic Package Manager to install pavucontrol (Pulse Audio Volume Controller). Use that application to set up your input device. Most built-in mics are mono. The default setting on the Input Control is to lock the R&L channel together. By reading the mono mic as stereo, PulseAudio cancels the input. Click on the middle button on the upper right of the control panel to unlock the R&L channel. Move either the left or right channel to 10 leaving the other channel about 90. You should now see the VU meter sensing sound. Now start Skype again. The test call should register your voice now.