Don't pry you will just muck up the internal trigger parts even more.

How will prying upwards gently on the dustcover muck up the trigger group? If anything, you are taking pressure off the trigger group.
The dustcover has two springs, an action spring and a striker spring. If the bolt carrier is forward that means the action spring isnt the problem. Its most likely the striker jammed in the rearward position, either by failing to be released by the sear because your trigger s**t the bed, or the sear is jammed upwards by a broken peice of trigger mech/debris(unlikely)
Now the striker is held in its rearmost position by the upwards pressure of the sear and sear spring, which is then released by the trigger, causing the striker to go forwards firing a round etc.
By prying upwards on the dust cover with the striker jammed backwards the most you can do is bend,or in worst case break, the striker spring guide rod, or cause the striker to hop off the sear connecting surface.
In that case the striker should move forwards, releasing the dustcover assembly. Pull down on the sear with a hooked tool at the same time you slowly pry upwards on the dustcover. It should go the last 2mm you need without damaging the rifle. Make sure you pull on the sear itself, not just the sear spring, which is the flat piece of springy metal underneath the sear.
Its not the ideal method of course, as it has the potential to bend/break the striker spring guide rod. It may also bend/break the striker,however that is highly highly unlikely as the striker is much thicker and heavier than the guide rod.
Once you have the dustcover off you should be able to see why the trigger is failing to release the striker. Post a picture and we should be able to get you sorted out.