94 Sentra neutral start switch??

My 94 Sentra, 1.6L manual trans, has 144K miles. When I came out of the grocery today, it wouldn't start- no clicks, no crank, but radio, seatbelts, and fan work. My wife popped the clutch when I pushed her (in the car!), and the car ran fine all the way home. Dead as a doornail in the driveway now, though. Is there a neutral start switch or starter relay (other than the solenoid) I should check? If so, where is it located? Can I short across the solenoid terminals to check it? I don't know if the two problems are related, but it often cuts out when I depress the clutch to downshift or stop at a light (but it normally restarts immediately). Thanks for your advice.

i have seen these relays go in the past, i forgot what there called at this moment. But it's a big Blue relay with 2 electrical plugs to it. It won't be inside the relay box, but if you looked in the relay box, it's 2x the size of the normal relays, you can start with that , i have seen them go , and when they do , you can't start the car normally.. just as you stated.

Gl..