Going from a "standard" triple (e.g. with large chainring of 52 or 53) to a compact double (with large chainring of 50), you will have to move the FD down a little bit. You'll also have to make some minor adjustments to the cable tension and limit screws. I'm assuming you are still using your existing triple-compatible shifters. Here's what I would do:
1) With the compact installed, reposition the FD. Article at http://parktool.com/repair/readhowto.asp?id=75
with info. Basically you want about a dime's thickness gap between the chainring and the FD.
2) Shift the shifters into the lowest ("granny") setting. Basically just push your small lever 'til it don't click no more
3) See article above about setting the Low limit screw
4) Take out any slack in the cable that results from moving the FD downward. It should be a small amount; might be able to get by with adjusting headtube adjusters if you have those; if not you'll need to loosen the pinch bolt on the FD, pull the slack, then re-tighten the pinch bolt.
5) See article above to adjust the High limit screw; the new High position will correspond to the old "middle" position of the triple. Basically what you are doing is setting the limit screw on the FD so that it's not possible to get into the former highest position of the shifter, e.g. "dead click" as you say. No adjustment is necessary to the shifter itself; when the FD screws are properly set it will take care of it.
Good luck; adjusting FDs is not terribly difficult but it can be very frustrating.