I guess the first thing I would do is see wether the hammer will fall while the trigger group is out of the gun. With the hammer cocked, and the safety off you can depress the disconnector (arm that sits on the front left side of the trigger group - push down on it to dis-engage) , and while containing the hammer so it doesn't fly forward, you can squeeze the trigger to check operation.
Simple things like the safety being imployed as mentioned, and of course make sure that the hammer is in cocked position prior to installing the trigger group.
If the system functions OK outside the receiver then make sure that the disconnector arm isn't bent. The tip of this arm should ride on thebottom of the left action arm. If it doesn't the disconnector will prevent funtioning of the trigger hammer.