I'm reading this and am concerned that the gas ram may not have lost pressure, that it may still be that the trigger is "stuck". I had that happen on Hatsan breakbarrels.
The hazard is, if the ram still has good pressure and the trigger goes off, one could get shot (if there is a pellet in the breech and the barrel is closed), or that the barrel swings back up violently, damaging the barrel or whatever is nearby.
So here is what I'd suggest:
1. Tie off the barrel in the "broken" or angled position to the stock. A belt might be perfect for this. Then clear the bore and breech of any pellets.
2. Unscrew the receiver from the stock. You might have to loosen or even untie the barrel so be careful in this state.
3. Close the barrel (straight out from the receiver, like you are shooting it), and put it in a safe position in case it fires and jumps. You should be able to see the Quattro trigger block. There should be a hole toward the back just above the trigger blade where one can see the sears and if they are engaged:
look around 18:45
If the sears are engaged, and they won't wiggle around if you press the trigger or push around in that hole with a small nail, then try to poke and prod to release the sears, to "fire" the gun. One dry fire won't kill it unless it is dead already.
4. If the sears are not engaged and thus loose in that hole, then see if you can push the piston forward or back. Look in that long slot under the receiver, forward of the trigger assembly for the piston. See if you can get a screwdriver blade in there and push it forward (or back). If you can slide it then yes, the gas ram is dead. The trigger sears ultimately grabs the piston, not the ram, so a moving piston confirms that the sears are loose, and that there is no ram pressure. If you can't move the piston, write back.