I want to place some white and black pieces on chessboard and then play that position against computer.

It always start the finish game (final position) against computer. 

Is there a way to do it with www.chess.com?

You cannot set up a starting board that way but if you were to play a friend an unrated game with the position you want, you'd be able to continue the game with the computer after it was over (drawn at the position you want).

for some reason i can set up a board on my iphone, but not on the website.  seems only the app allows this.  I use my iphone for this a lot.  

I see. I tried on my ipad2, it does not allow me  playing against computer. Needs Flash. Perhaps the only solution is to buy and d/l chess software that I need: starting position.

I dont have iphone. I dont intend to buy one. Strange that iphone allows this.

At least I can play on PC Windows XP because it is Flash enabled.