Car starting sometimes in neutral but sometimes wont start at all

Hello, When I bought my 1992 Jeep Cherokee Laredo, I was told that sometimes it started in Park and sometimes it didn’t. Anyways, it was fine, I just changed it to Neutral when this happened. However, I was coming out of class yesterday and my jeep wouldnt start in Park OR Neutral. Someone helped me and eventually I got it started in Neutral (now won’t start in Park at all). I am worrying that it may not start again in either of the gears.



I know why it wouldn’t start in Park, because of the switch, but why would it not start in Neutral also?



Also, I just got a new battery about two weeks ago. All the fluids in the car are fine as well

It’s the same park/neutral safety switch: http://www.autozone.com/N,16400218/shopping/partTypeResultSet.htm It could just be linkage adjustment.

That switch is called the Park/Neutral Safety switch. Which means it only allows the engine start if the transmission is in park or neutral. It sounds like P/N safety switch requires replacement.

Tester

Also, the cables that connect from the car to the car battery itself have calcium build up around the bolts and the area around the bolts are really dirty/grimy looking; could that affect the car’s ability to start??

Yes. Disconnect and file, or scrape, or wire brush, the corrosion off the cable ends and the battery terminals…