Welcome to GMT Nation...
I know the impulse to "Roll Your Eyes" will follow on with this inquiry, but there are Two Possible Issues worth Exploring:
(1) Is there any Chance that the Black Nylon Alignment Grommet inside of your Park Neutral Switch was first pulled off of the end of the Rotating PRNDL Armature without first slightly filing down the Outer Circumference of that Rod, just in front of the End?
If not... occasionally, that Center Black Piece can become Damaged and swell outwards enough to allow the Park-Neutral Switch body to get slipped completely off of the Old Transmission. The same thing can happen when re-installing the PNS Body back onto the Replacement 4L60E. If THAT Center Black Piece has been forced back over the second Armature Rod once too often without having lightly filed the OD of the Rod down to eliminate the Bulge that happens when the End Fastener gets tightened too much, then it will NOT be able to "Grip" the Round Steel Rod at its center.
Consequently, the Spring Loaded Internal Pawl will not be able to cycle back and forth inside of the Driver's Side of the Transmission Body and Shift ANY Gears in and out of their respective Positions. The Installation instructions for the New One should advise that it comes from the GM OEM Factory with a Removable, Thin Gray Metal Retainer put in place to secure that Black Internal Piece in the Correct PARK Position. Try NOT to disturb that Inner Black Nylon Grommet after removing the Retainer.
IMPORTANT.... CHOCK THE WHEELS FIRST BEFORE DOING THIS NEXT ACTION:
The idea is for you to FIRST Manually Cycle the Pawl with the short armature temporarily installed so you can ensure that the Internal Transmission Shifter AND the Internal Pawl Alignment is Definitely in the PARK Gear Position BEFORE attempting to slide the New Black Plastic PNS over the Rod to be secured with the Small Armature on the end of the Rod and that the (2) small Bolts to the Case are GENTLY tightened up to the 4L60E. Doing it this way will ensure that the Internal Black Nylon Center Piece will be in the PERFECT Position and will have a 'Good Grip' on that Rod. Push the New PNS on the Rod so that there is an EQUAL amount of Adjustable motion on BOTH sides of those Two Fasteners.
(2) The OTHER possibility is that even with the WHITE Grommet re-popped back onto the Ball End of the Shift Armature after the New (or Working) Park Neutral Switch has been -re-installed... if the CABLE HOUSING was NOT secured to the Shift Cable Support Bracket with that Weird Upside Down "Staple" having those Two, Sharp Ends to bend over in the Bracket... then the Internal Cable will have NOTHING to Resist itself against during Shifter Actuation.
Thus... No matter how you move the Shifter inside the Cab, even if the PNS Black Nylon Grommet has a 'Good Grip"... a Loose Cable Housing will prevent any of that Force from being exerted on the Shift Pawl Armature. If it is presently LOOSE and you've lost that Staple... Just get creative with some Sturdy Zip Ties and secure it onto the Support Bracket. It should work fine after that minor fix is done and the Cable Housing cannot come out.