Really a broad range of possible problems.
As the title says "park" and not neutral I'm going to a**ume automatic.
The NSS shouldn't have any effect on running. I does interrupt the starter relay ground except in PARK and NEUTRAL to prevent the starter from cranking the engine in gear, but there isn't an ignition interrupt built into it.
Lets go real basic: when running in PARK, after about 20 minutes of operation--in your case sitting and idling, what is the engine rpm with an external tach--not the dash tach. When the engine is fully warmed up and you put the transmission in DRIVE the engine should be idling at 700-750 rpm. When the engine isn't in drive it will be idling higher, but there is no specification for it. However, if the PARK/NEUTRAL idle is too low, the engine may be stalling out when you put the transmission into gear. So, check out the idle and post up what you find.
Another thing is the crank sensor aka CPS/CKP. If you have bad engine mounts its harness could be shorting out when you shift into gear and the engine torques. The crank sensor is mounted high on the driver's side of the bellhousing and the harness runs up from it. Also would be a good idea to unplug and plug it back in a few times to renew the connection. Without the signal from the crank sensor the ECU/PCM will not fire the spark, so any interruption in that signal and the engine dies.
There are critical grounds to your dipstick tube--the ICM (ignition control module--the thing the coil is clipped onto); the ECU/PCM; and the o2 sensor as well as other things ground there. Also, there is a braided strap that runs from the rear of the head, driver's side, to the firewall. That is the ONLY ground for the unibody, and it is critical. I recommend replacing the strap with a 4 or 2 gauge cable. For ALL the grounds, strip it down to bare metal, treat with an anti-corrosion agent, and make the connections TIGHT.
That should give you a few things to work on.
Post up what you find.
Good luck.
PS--welcome to
!