I haven't used Audacity before, is it possible that Audacity reverts your soundcard settings to "default" when it closes? And the default for inputs is usually "off" or at least turned down. (Edit: I just realized you may simply mean you used Audacity to monitor levels while setting elsewhere!)
What happens if you use the Gnome soundcard applet to adjust levels? (You may have to go into a menu to enable the recording sliders / switches. It's been a while since I played with that.) I'm running mine on a headless system, so no X. I use the alsamixer to set levels and save.
I assume if Darkice is staying running you actually have a /dev/dsp link. (IIRC Darkice still uses the OSS devices.) If not, you may just need to tell the system to load the OSS compatibility modules for alsa. Best bet would be to search Ubuntu Forums for that... Looking at my system, if you run 'lsmod' you should see snd_mixer_oss and snd_pcm_oss listed. I would expect Audacity doesn't use the old OSS method of accessing the soundcard, which could be why it works but not Darkice.
Another possibility, many people have had problems with Pulse Audio in the last couple of Ubuntu versions. I'm not sure how that interacts with something trying to access the sound card directly, but you could try removing it. Again, there are a number of threads on it on the Ubuntu Forums.