Your gradient bar is drawn only in setup(), so it overwritten and lost in the first draw() call (and the next ones, of course).
Perhaps you should have a draw() like:

void draw(){
  drawgradientbar ();
  move();
  movewhiterectangle ();
}

Note: instead of acting on transparency to make your gradient, you should rely on gray levels.

A few suggestions to start you off with:
- It's rectMode(CORNERS) not rectMode(CORNER)
- If you draw something then call background() then anything you've already drawn will be covered up.  background() needs to be the first thing in your draw() function.
- You never initialise barH to a value so it's zero everywhere at the moment, is that what you intended?

I suggest you try making your rectangles different colours so you can see what's going a bit better.  Make the different rectangles red and green so you can see everything working, get it right and then make them white.  Also use some println so you can tell what your variables are set to.  Trying to debug a white rectangle moving against a white background with no print outs is going to be next to impossible.

As said above...
And, again, try doing a color gradient instead of a transparency one. Against a monochrome background, it won't make much difference, except you will be able to see it, perhaps. I tried to replace stroke (0,0,0,transp); with stroke(255 - transp); for example, and got a strange result, although I could see something, so it is a kind of improvement... Perhaps transp should be reset, but then it isn't different of the i of the loop.