I want to point out for the sake of other users that the answer is more likely resetting Unity, as @brunopereira81 mentions below. So please, try that before tearing your hair out.

However, in my case, the answer was a need to downgrade the version of xorg and xserver-xorg. Once I did that, I had access to 3d again. (The answer to this question shows more of the background of how I went from a working installation to a broken one, and half-way back again) It ultimately stemmed from the xorg-edgers bug reported elsewhere.

Specifically, I had to reinstall xorg and xserver-xorg and ubuntu-desktop. After following a lot of recommendations on resetting compiz, dpkg-conf, etc, I found a couple key items:

1. For me at least, sudo apt-get remove xorg xserver-xorg ubuntu-desktop was insufficient, as this did not remove dependencies, even with autoclean and autoremove run after.


2. Rather, I had to use synaptic to do "complete remove" for each of these items.


3. After complete removal, it finally also removed all the dependencies, and they were now the correct, rolled-back versions.


4. Reinstalling ubuntu-desktop adds them back. There were about 5 items under xserver-xorg and xorg where it said it refused to install because another dependency was required. The solution to this was just to write down the name of the thing it would install, and select that before selecting the refusing item, which then allowed itself to be selected. It seemed strange to me this wasn't happening automatically, but there were only about 5 such cases, so it wasn't bad.

This series of operations fixed my 3d problems. (However, I am still having issues with libglib2 that will likely require a similar set of tracking down removals and installations.)