I have seen a couple of postings on forums recently mentioning that the stitch selector controls on Singer models 401, 500, or 600 no longer function. These three popular vintage machines share a similar mechanical structure and this is a common problem with all three models. The good news is that the problem is easily remedied.
When you rotate the stitch select knobs on the 401/500 or move the stitch select levers on the 600, you are causing metal collars to slide up or down on metal posts to select the desired stitch on the camstack. When the collars are not sufficiently lubricated, they stick to the posts and will no longer slide. If the collars don't slide, the control knobs/levers will not move, either.
The cure is to remove the top cover and dribble a drop or two of sewing machine oil down the two posts. The result won't be instantaneous - you should let the machine sit overnight before attempting to move the stitch select controls. Even that may not be enough, you might have to repeat the oil & wait cycle several times. If, after 3 times of oiling and waiting overnight, the collars still will not slide smoothly, try directing some hot air from a hair dryer toward the collars, that should make the collars expand enough to break loose.
Once the collars begin to exhibit a slight bit of movement, exercise them to work the oil in all around the area between the post and collar. Whatever you do, DON'T FORCE THE CONTROLS! If you bend or break the linkage between the control and the collar, it is no longer a simple, low-cost, do-it-yourself repair job.
After you have the stitch selector controls operating smoothly, make the posts part of your regular oiling routine.
Ed