Does not show Park, Neutral, third gear, or first gear.

No it doesn't. Any neutral safety switch is to stop a driver from starting a vehicle while said vehicle is in any gear other than P (park) or N (neutral) so the vehicle doesn't just start moving after startup. This doesn't effect the gears any whatsoever. Early US model vehicles had the neutral safety switch on the steering column and was connected to the shift lever. Late model automatic trans vehicles have this switch mounted directly to the transmission shift rod at the trans and mounted to it.

Your neutral safety switch is bad.The neutral safety switch is a safety device that only allows you to start your engine when the automatic transmission is in either Park or Neutral. ... This switch prevents you from starting the engine when the transmission is in any gear other than Park or Neutral.

Transmission range sensor , through electrical signals to the PCM ,it knows what gear the vehicle is in . Some all so call it a Park neutral switch , but it does more then that . The park neutral part of it won't allow the vehicle to start unless it is in park or neutral .

I had a a problem simliar to this that made it seem like it was the shift gear was the ignition switch,

The Neutral Safety switch monitors the position of your gear selector lever and either interrupts or allows the starting circuit in your car or truck to do its job. On newer vehicles it may also monitor the position of the brake pedal to make sure that the vehicle is in park or neutral AND that your foot is on the brake.

If your vehicle is equipped with a neutral safety switch, it should NOT start UNLESS the transmission is in Neutral or Park. On the other hand your vehicle SHOULD start when it is in Neutral or Park. If your car will start in Neutral but not in Park, you have a bad switch. Also, if your car or truck will only start by turning the key to the start position and wiggling the gear selector lever, your neutral safty switch is in need of replacement.

The nuetral safety switch is usually found near the gear shifter. If your car has the gear shift on the column, then the neutral safety switch is usully mounted on the steering column near the brake pedal. On floor mount or console mount vehicles you will find the nuetral safety switch mounted near or on the shifter mechanism.

If you think the car thinks it's in reverse when you have it in park, try dropping down a gear to neutral and try starting it. I own the same vehicle and I know it has an audible alarm if you try to move the gear shifter when the key is off and the selector is locked in place. I'd go through the entire range of the gear selector (both sides) to see if you might have a problem with the linkage or if the transmission has a problem that is not allowing it to go into park. It also has a park/neutral safety which which stops the vehicle from starting in any gears. The tcm mainly controls the functions of your transmission like the ecu (electronic control unit/computer) does with your engine controls. You may also be able to scan your vehicle for any trouble codes present in your transmission they will be either p0700-800 series code.

This is a common problem with all cars. Try to start the car in neutral. The neutral safety switch will not allow the starter to engage in any gear except park and neutral.
Another option is to firmly shift in and out of park several times. Just because the indicator shows park on the dashboard doesn't mean the neutral switch agrees with it. This firm shifting may realign the switch with the dasboard indicator. Good luck

try starting it in neutral. sometimes the neutral safety switch thinks you are just outside of park (aka in reverse). this switch will not allow the car to start in any gear except park and neutral. also, try shifting firmly in and out of park several times. this may trip the switch. good luck

Sort of...
There is a safety neutral switch that will only allow the car to start in park and neutral. If it starts in other gears or Not in park, then switch needs to be replaced

ya the neutral safety switch would cause that if the car doesnt think its in park or neutral it wont start