Will hearing but not listening to a video mentor help me learn? I have a A+ video mentor that I got through school. I was wondering if playing the videos as if they were music and just going about the rest of my tasks on the computer would help me to learn the information. Thank you.
From experience and some knowledge gathered from all over the place, yes and no. For example, if you want to do two things that are both mind-engaging, you'll probably end up doing both sloppily, or one much better than the other. But if one task is mundane and other mind engaging, like listening to music and doing math problem, or listening to a lecture and cleaning a room, you can probably do them both with no problem.

Also, "multitasking" does not actually exist. You can find many articles on this subject. What we think of as multitasking is actually task-switching. Your brain does not do two things at once, but switches from one thing to another. Task-switching is demanding a lot of energy, so some people may feel tired from it. 

Some people are better than the other at task-switching, and can do it for some time without getting that much tired. I don't know how good you are at it, but you can try. If you haven't trained your mind to work efficiently like that, you might get better after some time, or just keep doing one thing at a time. (I know person who wasn't much of a "multitasker" but got better after some years of practically forcing it.) Hope this helps.