You cut a big hole in the door and pulled the whole piece out. 
The screws were painted over.
Good guesses. But no and no.
The poke hole for the inside lever is underneath the bezel, looks like the lock was installed poorly. Sometimes, it is possible to get a flexible poke tool, (I have used a broken pick end, which is a thin spring steel).
Sometimes, you can push or prod the lock front towards the door and get a bit more room to find the poke release in the inside.
To correct the situation when you install it, While off the door, remove the outside lever and the bezel ring will come off the lock body, there will be a screw on nut/washer thing you can back out, then put the bezel and lever back on like normal.
There is always a hacksaw.
Correct. The door is a little wider than average, which contributed to this problem. Pushing on the inside of the bezel revealed just enough of the hole to slip a wire into.