EDIT:Knowticed after I posted that Buffdog beat me to it!!
My first thought was I would suspect that there is something touching the trigger mechanism, perhaps the stock?
But then it hit me, I would check to make sure the rear pilar is there and not too short. If the pillar is too short the trigger assembly may not be engaging the sear correctly once it's tight. That's probably why if you assemble the action screws loose it works but then if you tighten it you may have issues with the engagement of the trigger parts.
Take the rifle apart, and install the trigger guard to the action out of the stock. Insert the front action screw snug. Then measure the distance in between the bottom of the reciever and the top of the trigger guard in between where the rear action screw goes. Then measure the rear pillar in the stock. If you can pop it out and measure it with a micrometer. If the pillar from the stock is quite a bit shorter your action will go together crooked and may cause accuracy/and trigger issues.
Anyhow, that would be my guess on what's going on, although I'm sure someone with WAY more knowledge then me may have a better idea of what the problem is.
Just my thoughts.
Steve