First off - these variable names are a little meaningless:

1. int a=200;
2. int b=height+10;
3. int c=200;
4. int d=height+390;

What do they represent? e.g. I'm guessing something like paddleX, paddleY, paddleWidth, paddleHeight.  Generic and meaningless variable names are a bad idea!

Secondly the use of 'height' in the above code is redundant as it is not set until after setup() is called:

1. int foo = height;
2. void setup() {
3.   println("before: " + foo);
4.   println("after: " + height); //default is: size(100,100);
   
5. }

Not sure what ballpaddle1() is meant to be doing but at the moment it's stopping your ball from moving:

  if (ballpaddle=true) {

Here you set the value of ballpaddle to 'true' rather than testing its value like so:

  if (ballpaddle == true) {

You've also got an empty condition within moveball().  I'd ditch the superfluous ballpaddle1() and concentrate on figuring out the condition required here.  If you think about it you should be able to work it out.  Here's how I'd define it verbally: if the ball's height is greater than the paddle top's y position and the ball's x position is between the paddle's left and right x positions make it bounce.

void setup(){
  size(400,400);
}

void draw(){
  background(255,102,255);
  ball();
  moveball();
  bounceball();
  paddle();
  movepaddle();
}

void ball(){
  fill(153,51,255);
  stroke(153,51,255);
  ellipse(x,y,ballwidth,ballheight);
  smooth();
}

void moveball(){
  x=x+speedx;
  y=y+speedy;
  if (y>height+(ballwidth/2)){
    println("Game Over!");
    noLoop();
  }
}

void bounceball(){
  if((x>width-8)||(x<8||(y<8))){
    speedx=-speedx;
    speedy=-speedy;
  }
   if(ballheight>=paddley && x<=paddlex && x>=(paddlex+40)){
    ballpaddle=true;
    speedx=-speedx;
    speedy=-speedy;
  }
  if (ballpaddle==true){
    speedx=-speedx;
    speedy=-speedy;
  }
}

void paddle(){
  fill(0,204,255);
  stroke(0,204,255);
  rect(paddlex,paddley+height,40,20);
  rectMode(CENTER);
}

void movepaddle(){
  if (keyPressed){
    if(key=='a'||key=='A'){
      paddlex=paddlex-speed;
    } else if((key=='d'||key=='D')){
      paddlex=paddlex+speed;
    }
  }
  if ((paddlex<20)){
    paddlex=paddlex+speed;
  }else if((paddlex>width-20)){
    paddlex=paddlex-speed;
  }
}

 

The second condition in this section of code is pointless and actually reverses the effect of the first condition:

1.   if(ballheight>=paddley && x<=paddlex && x>=(paddlex+40)){
2.     ballpaddle=true;
3.     speedx=-speedx;
4.     speedy=-speedy;
5.   }
6.   if (ballpaddle==true){
7.     speedx=-speedx;
8.     speedy=-speedy;
9.   }

You seem to be tacking stuff on here and there in the hope that you can get it working...  When you get to this state it's often worth starting from scratch (and thinking carefully about variable names*) in a new sketch and implementing each bit of functionality one step at a time - e.g. get the ball moving and bouncing off the sides.  Then insert the paddle and get that moving with keyboard controls; then finally figure out the collision detection with the paddle.

Your hit condition fails for a couple of reasons:

1.  What is the 'ballheight' variable you're testing paddley against?  (*hint: perhaps ballwidth and ballheight could be replaced with a single 'radius' variable; then you might not get confused).

2.  x<=paddlex && x>=(paddlex+40)
This tests whether the ball's x position doesn't correspond with the paddle's x position!