Well, as headless, dispense of the [not needed] boinc-manager gui part and see what happens [Just sudo apt-get install boinc-client]. Most all commands can be passed with the boinccmd tool or you could fetch BOINCTUI for terminal, a text only BM, for the easy way out.

Try just sudo apt-get boinc . Maybe some other headless running Ubuntu server operator can chime in.

edit: Of course you could also just fetch the Berkeley .sh kit... less convenient.

I have 2 Ubuntu servers running headless. Used

sudo apt-get install boinc-client

and X was NOT installed. Also do not remember much else being installed. boinc-manager does require X and a desktop GUI.

From your favorite browser, access the WCG homepage (http://www.worldcommunitygrid.org)
Click on "Settings", then click on "My Profile"
Enter your member name and password and click "Enter"
Locate your Weak Account Key. The weak account key is about 38 alphanumeric characters with an underscore after the first 6 characters; substitute that in the command below where it says WeakAccountKey
On the server enter the following commands: Note, the first command should move you to the BOINC directory. Be sure that you are in the directory where you installed BOINC when you enter the command.

That should get you attached to WCG and start downloading some work.

Here is a link to some other useful commands for boinccmd http://boincfaq.mundayweb.com/index.php?language=1&view=503

Hope that helps, let us know if you need more assistance.
CaptainJack