If you’re using the Mac version of LockDown Browser and the “Begin Exam” button seems to do nothing (or it takes you back to a previous step), please upgrade LockDown Browser to version 1.0.8.05 and higher. The problem you're experiencing can sometimes occur after a Mac awakes from being put into Sleep mode, but has been fixed in LockDown Browser version 1.0.8.05.
To upgrade, start LockDown Browser, select “About” in the toolbar, and then click “Check for Update.” The version will be displayed and you will be able to download a newer version if one is available.