The way you're trying to achieve this would take away a lot of resources.
Better create (or load) 2-3 (I don't think you need more than three) "random noise" textures and cycle through them. Randomly creating screen-filling noise in every frame would be waaay too heavy.
So what you can do is create those frames at program start or when you need them (still, only once, and keep them in memory if you need it more often), by filling each pixel of each frame with a random value. You could also just create those textures in some image manipulation software that offers a noise-filter and load them as textures.
Then you cycle through those few frames, it's unlikely that anyone will notice that you're using the same non-random textures over and over again.
At least that's how I would do it.
P.S.
I only took a quick glance at your code, but when you call sf::Texture::loadFromImage(), you're not adding something to your Texture, but resetting it. That's why you only draw one of your dots each frame. (Also there are other ways to properly do this, but you should rather do something like mentioned above.)
[edit]
Also you should read about the difference of Events and Input using sf::Keyboard and alike, it's not supposed to be inside the event loop. I suppose the tutorials would be a good start.