My first Brother had dials like yours. I had to make labels for each dial because I kept forgetting what each one did. I looked up the manual for your machine, and it shows that you have a Pattern Selection dial. Could this be what you're turning to get the needle to move? Here's the manual URL in case you didn't get one with your machine. And please forgive me if my questions are stupid.
http://www.brother-usa.com/ModelDocu..._ENES_1565.PDF
Editted to add: Never mind the above question. I saw on page 25 of this manual that your stitch width dial does regulate the position of the needle. It also says "When the Straight or Triple Stretch Stitch is selected, the needle position can be changed
from left to right by adjusting the stitch width dial." So it looks like as long as you have selected the straight or triple stretch stitch (neither of which have a 'width') you should be able to adjust the needle position. Sounds like it is definitely not working.