Could I please have a draw on the last game I played?
no 50 move rule

You have to claim it. The "offer draw" button turns into a "claim draw" button if the conditions of a draw have been met.

Yeah, the 50 move rule definitely applied. That's too bad about losing on time because you didn't know to claim it....
http://www.chess.com/livechess/game.html?id=187482364

This happened with someone else, only with this one, he actually claimed a draw;
http://www.chess.com/forum/view/help-support/i-want-to-make-an-appeal

You could have also claimed it due to repetition. That was a long repetition bout of three positions if i might say so.

Hmm... basically all you and your opponent did for 170+ moves was cycle between three positions. Assuming your opponent knew that clicking on the Draw button would have immediately ended the game as a draw, it was very cheesy of him to keep playing. But, I suppose this isn't an ethics question.
As others have already said, use that Draw button. If a three-fold repetition or the 50 Move Rule applies, you'll get an immediate draw. A good alternative is to play games with a 1- or 2-second time increment. That will discourage players from trying to run your clock out in a dead drawn position.

tazerdadog: It's unlikely this has ever made a difference, but, no, the rules do not say anything about castling resetting the count for the 50-move rule - only captures and pawn moves apply. Castling does become a factor for another type of draw claim, that being for three-fold repetitions. A three-fold repetition requires that the same position with the same set of legal moves occurs three times. You can have a position repeat where, due to the loss of the castling (or en passant) privilege, it is not considered a repetition. A good example of this occurred in Fischer-Najdorf, Varna Olympic 1962 (game #40 in "My 60 Memorable Games") where Fischer played 16. Ng7+ Ke7 17. Nf5 Ke8, reaching the same position but taking away Najdorf's right to castle. It would have been interesting to see what happened next if Fischer repeated the position one more time and Najdorf tried to claim a draw, but Fischer didn't test this - kind of surprising, actually, considering how much he liked to start arguments.

ok, that's how I thought it worked... no need to shake the foundation of all of my chess knowledge yet!

Thinking about it, resetting the 50-move count after a pawn move seems like a bad rule. For one thing, moving a pawn doesn't change the endgame, it's just making progress, the same way getting the other king to the edge of the board can be considered making progress. The real problem with the rule, though, is that it can be abused. For example, see the following position:
Any experienced player knows the above position is a dead draw, but a not too scrupulous White player can drag out the game up to 250 more moves: (a) make 49 random moves (just don't repeat any position 3 times) (b) play h3 on the 50th move (c) make 49 more random moves (d) play h4 on the 100th move (e) make 49 more random moves (f) play h5 (g) make 49 more random moves (h) play h6 (i) make 49 more random moves (j) play h7. Great plan if you are up on time in a blitz game, eh?
Of course, this is just one of many dead drawn endings I could have selected to make my point. Not having pawn moves reset the 50-move count would eliminate this nonsense.

Captures and pawn moves reset the count because they are irreversible moves -- for this reason, it's wholly appropriate and arguably castling should maybe also count.
Interestingly, when we talk about three-fold repetition I don't think that whether or not en passant was an option or not factors and I think maybe it should. For example:

Black will capture the pawn long before white can play his 49th move. Don't feel like checking the rest of your statements...

mathot: Add a light-squared bishop then. Now there is no question White can drag it out for up to 300 moves.
As for irreversible moves (mentioned by TheGrobe), it makes sense to consider then for three-fold repetitions, but I don't see the relevance for the 50-move rule. You can view a pawn advance as making progress, but that isn't always the case. In fact, a badly timed pawn advance sometimes turns a win into a draw. The real measure of making progress is if you are moving closer to a checkmate or a simplification to an easier win.
My last game it didn't register a draw it was 210 moves and I had perpetual. Why didn't the game draw? Way over 50 moves!