After reading what you had posted, I do agree that if it was some kind of permissions issues, nothing would print at all. Knowing that it prints some of the times, and not all, would lead me to believe that it is something else.
Trying a different browser, as phreekd
suggested is a good test.
Another set of tests would be printing from other applications (notepad, word, excel, adobe reader, etc), as well as doing a test print from the printer in control panel.
If those all print without any issues (no random items not printing), then that would fully rule out permissions, and point it to an application issue (in this case, Chrome).
So when you get a hold of the laptop later to test things from IE, if you have a little more time, see if you can run some test prints from other applications and see how that goes.
--Brian