Does White have a won game?

[Site "Chess.com"]
[Date "2011.10.15"]
[White "Player"]
[Black "Computer - Hard"]
 1. d4 f5 2. h3 Nf6 3. g4 Nc6 4. gxf5 d5 5. c3 Bxf5 6. Bg2 Qd6 7. Nf3 O-O-O 8. e3 e5 9. Ng5 Qd7 10. b3 exd4 11. cxd4 h6 12. Nf3 Bb4+ 13. Bd2 Qe6 14. O-O Kb8 15. a3 Bd6 16. b4 Bxh3 17. Nc3 Bxg2 18. Kxg2 Ne4 19. Nxe4 Qxe4 20. Rh1 Qg4+ 21. Kf1 Rhf8 22. Nh4 Qe6 23. f3 g5 24. Ng2 g4 25. f4 Rf6 26. b5 Ne7 27. a4 Nf5 28. a5 Ng3+ 29. Kg1 Nxh1 30. Kxh1 g3 31. Kg1 Qh3 32. Kf1 Qh1+ 33. Ke2 Qxg2+ 34. Kd3 Qe4+ 35. Kc3 c5 36. bxc6

I was playing as white against the 2000+ rated computer.  The computer stalled out at this move and was perpetually thinking- at move 36 (for over 30 minutes).  Does white have a won game? PLEASE help me analyze the variations of the end game- and possibly the entire game to help me understand this game fully.

Sorry, I just never posted a game before, and I was testing how to do it using your game

But, it does look like black wins after 36...Rc8

after blacks rc8 .....rb1 looks ok but entire position seems to favour black with passed pawn on g6

Black's a rook up...

Not a chance for white.

I hope you're not gonna say "First!"...