It really just depends on how busy they are. I haven't personally sent anything back to Colt, but I've heard of people getting firearms back within a couple weeks and I have heard of some not getting their firearms back for a couple years... I don't know what the real story is with the latter, but I do know that it just depends on how backed up they are.
If I were you, I would try to fix the issue myself. When you say the trigger doesn't reset, does that mean the disconnector is engaging the hammer and not releasing it? In full auto, the disconnector shouldn't even touch the hammer. Or is the trigger sear skipping the hammer, thus the hammer continues to fall forward even when the trigger is released (not touched)?
You can get a full genuine Colt replacement parts set from Specialized Armament Warehouse - http://www.specializedarmament.com/
, but that's going to cost you money.
Also what ammo are you running and are you using the factory "H" buffer?