As soon as my game starts, it freezes on the main screen. It never shows any animation and plays no sound. It just shows the main "Syndicate Plus" screen.

The screen just says "Syndicate" for me. When I press Esc, the color pallette shifts briefly, and then Dosbox quits. Is it the same for you?

Good explanation. From it, it is clear that the game works (as it reacts on keys as it should).
But - the game shows only background, on which normally a selection between Syndicate and AR is.drawn.

So your graphics card only draws first frame, and then stops drawing the image. It is clearly video driver issue.

Besides updating your driver, you can also change output type in DOSBox config file. You will most likely find that only one output type is broken, all other will work.

How to change DOSBox config - use a search engine.

Getting exactly the same problem on launch, on both my laptop and gaming PC.