On auto car, the interlocks are shift lever switch and the security system, both of which interlock the starter-cut relay.
Check
this post for where to locate the starter cut relay and schematic of the starter circuit.
Or check the on-line manual
http://www.nsxprime.com/FAQ/Reference/1991_svcman/1991servman.pdf go to page 1063
You either have
a) no power to the 'hot' side of the relay (which would be an ignition switch problem or main fuse #29) - with keyswitch in 'start'position check for +12V at the black/white wire either at the ignition switch itself or the starter cut relay (located next to the security module behind the glove box - need to remove the glove box to access); if no +12 then bad ignition switch (known!) or fuse 29.
b) no ground to the 'low' side of the relay - test by cranking while directly grounding the black/green wire from your shift position switch; if it works, you either have a bad or disconnected switch or a security interlock; to test for which, ground the black/yellow wire at the shift switch - if it works, problem in security - if not, bad switch.
c) if neither power or ground to relay is problem, possibly bad relay.
I suspect something to do with the shift switch since you have removed the console to remove radio - possibly got disconnected or knocked out of whack?
Do you have keyless entry? Close hood & arm/disarm the system (or lock unlock manually with key) and test again.