Ok ,

you said the tranny dont. how do you know that.?
starting (its really cranking) works in park and neutral both.
this is normal.
so since you got to N, that means it not the PARK lockout feature failing.
so if it shifts to N, and cranks and then starts and they you'd shift to D, what happens then in D?>?????????????
you never said !

if car runs ok started in N but only fails to crank in park
that means the P/N switch is bad, (p/n park neutral crank start line fails in park but not Neutral means the P side is worn out, as all do )