I have been struggling to import a couple large classes (1.4 GB) from Moodle 1.9 to 2.3. Tried backing up only a certain portion of the class, such as the quizzes, but still it gave a database error or just hung and didn't do anything.
First solution, was to NOT use Internet Explorer. Make sure no one is using that for Moodle. We chose to use Chrome.
Second thing I did was to create a "new course" on Moodle 1.9 and import (not restore) the large course from the same Moodle 1.9 server. I then did a backup of the "new course" in Moodle 1.9. The file size went from 1.4 GB to less than .6 GB. I then took that backup and restored it into the Moodle 2.3 server and everything worked great.
Each semester we do a backup of the courses, and then restore them into an empty course shell, so we now have a copy of 7 years worth of data. I am thinking that caused some of the problem.
Hope this helps someone.