The code doesn't seem complete. The lack of } at the end is suspicious...
Explaining what problem(s) you have can help us to help you, too...

Two obvious problems in your new code:
- you wrote Draw() instead of draw(), so nothing will be drawn. (same problem in the old code)
- you have a block of code after draw that's part of no functions, so it won't be called either.

Another problem: you draw 3x3 rects on each pixel of a line...

Here is a working version of your code:

1. int gen = 0;
2. int[] oldGen;
3. int[] newGen;
4. int genWidth;
5. int CELL_SIZE = 3;
6.  
7. void setup()
8. {
9.   size(1200, 600);
10.   background(0);
11.   noStroke();
12. //  frameRate(10);
13.   
14.   genWidth = width / CELL_SIZE;
15.   oldGen = new int[genWidth];
16.   newGen = new int[genWidth];
17.  
18.   //randomly initialize
19.   for (int i=0; i<genWidth; i++)
20.   {
21.     oldGen[i] = int(0.5+random(1));
22.     newGen[i] = int(0.5+random(1));
23.   }
24. }
25.  
26. void draw()
27. {
28.   //calculate new generation
29.   for (int i=0; i<genWidth; i++)
30.   {
31.     int prevCA = oldGen[(i-1+genWidth) % genWidth];
32.     int currCA = oldGen[i];
33.     int nextCA = oldGen[(i+1) % genWidth];
34.     {
35.       if (currCA ==1)
36.       {
37.         if (nextCA ==1)
38.         {
39.           if (prevCA==1)
40.           {
41.             newGen[i]=1;
42.           }
43.           else
44.           {
45.             newGen[i]=1;
46.           }
47.         }
48.         else
49.         {
50.           newGen[i]=0;
51.         }
52.       }
53.       else
54.       {
55.         newGen[i]=1;
56.       }
57.  
58.       if (currCA ==1)
59.         if (nextCA ==1)
60.         {
61.           if (prevCA==1)
62.           {
63.             newGen[i]=0;
64.           }
65.           else
66.           {
67.             newGen[i]=0;
68.           }
69.         }
70.         else
71.         {
72.           newGen[i]=1;
73.         }
74.  
75.       else
76.       {
77.         newGen[i]=1;
78.       }
79.     }
80.   }
81.  
82.   //draw new generation
83.   for (int i = 0; i < genWidth; i++)
84.   {
85.     if (newGen[i] == 1)
86.     {
87.       fill(255);
88.     }
89.     else
90.     {
91.       fill(0);
92.     }
93.  
94.     rect(i * CELL_SIZE, gen * CELL_SIZE, CELL_SIZE, CELL_SIZE);
95.   }
96.   
97.   //replace the old generation with the new generation
98.   arrayCopy(newGen, oldGen);
99.  
100.   //increment the new generation count
101.   gen++;
102.   if (gen == height / CELL_SIZE)
103.   {
104.     noLoop();
105.     println("Done");
106.   }
107. }

Except the automaton seems quite bland, each line is the previous one, shifted by one cell...
You might need to tweak the rules...

Thanks a lot PhiLo,