EDIT AT 6:15;
Corrected the way latch works, and added picture.
Does the inside handle open the door with no issues?
The inside handle pushes on the lever that the outside handle is connected to.
If the inside handle works, then you need to adjust the outside rod at the threadded end.
I would disconnect the rod from the latch, lift up on lever to remove all play, pull down on the rod to remove all play, and thread the ftting up the rod until the fitting just fits in the hole in the lever, and install it,
If outside handle still won't open the door, then you will need to look at the push button part of outside handle.
I have read comments by many that the push button has been problemaitic.
My outside handle stopped releasing the latch. I had to pull the latch, and clean & lubricate it.