Obviously check battery first. Use a known good fully charged battery
Recheck all wiring that you fixed or may have inadvertently messed with. A tight clean mechanical connection equals good electrical connection.
Check Starter relay found in the PDC (Power Distribution Center in engine compartment passenger side front)
Park/Neutral switch as you've already mentioned.
Can you pull any codes? Stored or Pending.
Has the battery been run down, charged in place, jumped by another vehicle since you did cable repairs?
These Chrysler PCM's are so sensitive to voltage/current changes that happen when batteries are run all the way down or sometimes when being jumped off. Even some batteries that seem to turn over the engine may cause problems if a cell is marginal and start voltage is not quite there. Killing PCM's often happens after battery problems particularly after batteries being run down all the way and jumping off. However, I don't think a bad PCM will cause the starter to not turn over but not 100% sure.
I remember one time when I swapped a head and put it back together that I had a no start situation. I finally pulled starter and left it hanging by cables, turned ignition and it spun, then put it back on and it fired right up. Not sure what that problem was....maybe the solenoid was stuck or something..... but worth a try if all else fails.
(02 Blue WJ 4x4 4.7L Laredo project 147K) (01 Blue WJ 4x4 4.0L Laredo 38K on engine/tranny... wife's) (99 Black WJ 4.0L Laredo Project 38K needs engine/tranny) (00 Red WJ 4x4 4.7L Limited project 200K) (97 Grey ZJ 4x4 5.2L Orvis project 200K) (97 White ZJ 5.2L Limited project 125K) (98 Green ZJ Limited crashed parts vehicle 195K) (97 Grey ZJ 5.2L Laredo 130K) (& with great fondness....Ole Yeller....my 89 Yellow Grand Wagoneer....dearly departed) Snellville, GA