The key to assembling the gun's trigger mechanism back together is those 90 degree angle springs. These are really tricky, since the 2 springs require 4 points of contact to be in place when you put the box halves together.Here's a more visual explanation.
Everything in that second picture looks perfectly fine except for those
angled springs, which are the ones I've circled in this here photo:

NOTE: There should be
2 of these, one on both sides of the piston sear, facing in reverse directions. Your photo shows that there's only
1 spring.
These springs are key to keep the piston sear centered. What happens is that, when you pull the trigger, that sear violently rotates when the piston shoots forward. The springs push back against the sear when it rotates, bringing it back to its original 90 degree position.
In order for the springs to work correctly, the springs need to be able to push on
(1) the piston sear, and
(2) the trigger box. The trigger box is the base for the springs to push on. It's like the ground to your feet, allowing you to jump.
So, when you look at one of those angled springs, you'll notice that on one end of it, it's
long and straight, while the other end is
bent at a 90 degree angle. The
Long end must push against the piston sear's nub, while the
Bent end must be tucked INSIDE of the shell when you put the second half over it, allowing it to push against the shell. Here's a photo:

Your spring is facing in the correct direction, having its Bent end pointing
away from the piston sear. This is what you want. So, that means that the spring that
should be behind the piston sear right now should be pointing
into the table,
away from the piston sear, while the spring that's closest to us should have it's Bend end pointing
away from the table,
away away from the piston sear, like it already is.
You must do this with BOTH of the angled springs on BOTH sides of the sear. The springs will push the nubs on
opposing directions, allowing the piston sear to sit at a 90 degree angle. The tricky part is
tucking in both of the Bent ends inside of the shell without have the Straight end slip off the nub while you put the shell together.This doesn't always happen the first time you try it. It took me nearly an hour and a half to put mine together correctly the first time. You might need to physically bend the spring by hand in order for it to not slip off the piston sear's nub, like I had to do.