Mortise Lock
Something is going on making the lock stick when locking when the slider is not closed. Seems like when it's closed is doesn't do that. Also, the key won't turn at all so that seems to be jammed. Before I got the new parts from my latest order, the key just spun freely. Does it sound like swapping out the mortise make sense?
It does sound like it could be a mortise problem, but there is one sure-fire way to check. I recommend using a flat head screwdriver to attempt to throw the mortise manually. If it still hangs up, then you found your culprit. The 82-238 can replace it.
If it works fine, though, then something's up with the handle. Check the key lock to make sure it's oriented properly in the handle. Sometimes they can come askew during installation.
Sure, you pretty much just pop it in that square hole and turn it, just like you're locking/unlocking the door. As long as the blade of the screwdriver is wide enough it should do the same thing--assuming it's still functional, of course.