On line 641 of your page you have the following code:
nextSlide = ActSlide-1;
prevSlide = ActSlide+1;
In this line:
32 is the keycode for the space bar.
return false; two lines later is what is preventing anything from happening when you press it.
Whilst it is important to not neglect keyboard users (for example when you have a proper image gallery), in this case I'm not sure that this extra functionality is warranted.
The easiest thing might be to just remove it.