If you tried in positions other than PARK, then I wouldn't think it IS a NSSW problem, also the Orange indicator really has nothing at all to do with it, but you can adjust that too
On an '03, one of those "black box things" is actually your starter relay so, yea, make sure they're plugged in!
Next I'd be looking elsewhere... It could be the key switch, relay, wiring, even the starter itself (these things usually just get worst as time goes on and you might end-up stranded...).
Carry a hammer with you and use it to "rap" on the starter a few times. This can reseat the Bendix or brushes sometimes on a failing starter. But, maybe it's time for some good ole troubleshootin'
Take a test light and see if there's power being sent to the Bendix (on the starter) when you rotate the key. Then, you can decide if the problem lies on the "key side" or the starter. Do it now, while things work, to know what to expect to see and where to check (the small yellow wire on the starter I think)