Rules

If you touch the ball on the tee but the ball stays on the tee does this count as a shot.

No , balls not in play until you make a swing.

Many thanks from another fountain of knowledge on this site.

You can knock it off the tee too and it still doesn't count as a shot

Thanks for the info ....

Stephen,

Not true about passing the marker.  The ball is not in play until you have made a swing at it. 

Regarding your question, the answer is none.  If you strike the tee marker the shot must be replayed without penalty

 A ball is not considered in play until a stroke has been made, so when the ball is sitting on the tee, it's not yet in play. A waggle of the club, or shaky hands, or any similar move that results in bumping the ball off the tee is not a stroke. Intent is the key - remember, a swing is only a stroke if the intent is to hit the ball  .So even if you take a practise swing and hit the ball 100 yards it can be re-teed without penalty.

There is no penalty, it does not count as a stroke, and the ball is re-teed and played (see Rule 11-3).

Here's a scenario in which it would, however, add a stroke to your score: You address the ball, take a mighty rip - and look down to see the ball sitting untouched on the tee. Your intent was to the hit the ball, so even though you missed, it's a stroke. Because you've taken a stroke, the ball is now in play, even though it's still sitting on the tee.

So you address the ball a second time, and in waggling the club bump the ball off the tee. Guess what - now it counts as a stroke because Rule 18-2a applies. Because the ball was in play, you must assess a penalty stroke for touching a ball at rest with your equipment. 

One stroke penalty.