Outside Door Handles

Just guessing, push button far as it will go and latch doesn't pop, or maybe it did but button wouldn't
Should be a tiny little hole in the latch side of the door, just above the latch. That's where a allen wrench goes in and loosens/re-tightens to adjust length of the actuator rod going down to the latch mechanism.

The button has play in it when the rod is attached. When disconnected the play in the button is not there....The latch to the inside is working fine.

used latch? a lot of those latches are year specific, also did you clean & service said latch before installing? that thing should snap when being operated.
How does your latch work from the inside?
This could be as simple as the lock mechanism portion of this latch is stuck causing the outside door handle not to work.(how they are designed)
clean/ lubrication is your friend on these things ,Lawrence