As a couple other people have said, this is a belt-driven machine, although the motor is internal, so the belt is mostly hidden. I think your needle isn't going up and down because your belt is missing - you can kind of see in the second picture where it ought to be. The bobbin winder wheel runs against the belt, when it's there.
I have a definite soft spot for the 328 since I learned to sew on my Mom's. I like the way the light bulges out on the front. I wish I had realized a few years ago that one of my life goals was going to be to own a treadle sewing machine that could do fancy stitches; I wouldn't have let her give it away if I had realized. Yours appears to be in great condition - I hope you get it stitching!