Since it started just fine once, I doubt it's the starter "all of a sudden" if you're getting absolute zero response to turning the key now (i.e. to dmjlambert's question - I have the same question, but will assume you mean no spinning, whining, grinding or Anything happens when you turn the key). Sounds more like an electrical issue to me.
I'll just throw this out here, not to insult your intelligence, rather to highlight my lack thereof - because I've done this... Replaced an engine, and racked my brains for days trying to figure out why it wouldn't start only to realize that I had put it in neutral to center it under the home-made chain-fall hoist I'd rigged up. I felt like a moron. Anyway, to my credit (I need some at this point), it did fire right up in Park
Anyway, I'll assume this isn't your mistake because you're already talking about the possibility of a neutral safety switch problem (I hadn't even considered it, then again, I think I was in my early 20's at the time, and in a "big rush"!) But it's worth checking to make sure it hasn't slipped even slightly out of park... I could've saved a lot of time if I'd only done that. Wiggle the shift lever while attempting to crank is also not a bad idea to at least eliminate the possible causes.
Ok, true confession session is now over
Assuming you're in Park, yes, could be a faulty neutral safety switch, but, like the starter theory, odd that it would work, then not work all of a sudden. That's the only reason I mention triple checking it's not slightly out of Park somehow.
EDIT: Btw, welcome to the site! Not recently, but have spent lots of time in Kentucky, just up the road from you "a piece".. (Morehead, Hillsboro, Flemingsburg area). Lots of family there.