RhettMan, Don't know if you really mean a tile drain, or just a drainline? Don't know if all your drainline is under the deck?
I've had the same situation, but I was able to find the drainline and cut it at the midway point. Turn your valve on. If the water comes from your right, go that direction. If it doesn't, go the other direction.
Hopefully your deck boards are screwed down, instead of nailed. I had one that I had to remove the deck boards to get to it.
You mentioned stuff going under the new addition. I would definitely reroute around it.
Some of these issues just take patience. Stick with it. You will eventually find it. I've found that I usually do better after I've slept on it a night.