Most likely your clutch is finished. Parts are worn beyond specs. Or, check the clutch cylinder for air or low fluid, if cable, check adjustment.
Switch, circuit, shift motor
A capacitor start motor is a split phase motor that uses a capacitor in series with the start winding to cause a greater phase shift, resulting in greater starting torque. It uses a centrifugal switch to switch out the start winding and capacitor once the motor is up to speed. I assume this switch is what you're referring to as a "relay".
All vehicles with automatic transmissions have a safety switch to prevent starting when the shift lever is not in the "Park" position. If you vehicle requires extra pressure or attention to engage the switch, it is because the shift mechanism is loose and/or misaligned.
Check the motor mounts
It could be the shift motor on the T Case. Or it could be the automatic shift button switch on the dash.
Check fuses: All systems you mentioned operate with out ignition switch on. Brake lights and shift interlock are a common circuit--check to see if brake lights are working--if not could be stop light switch or again fuse Try turning key to 1st position (unlock) without starting engine then shift to neutral to start, then shift to Drive to move vehicle
this is a GT with floor shift and 3800 engine
Some systems require the engine be at low power to shift, the easy way to ensure this is to use a vacuum switch Also some cases use vacuum to actually shift into 4WD
the switch is inside the back cover, but you should check the shift drum. the end of the shift drum has a slot in which the neutral switch sets in, and on my rancher the end of the shift drum was broke so when the quad is in neutral the switch said it was in gear you pretty much have to completely disassemble the whole engine and tranny to change the shift drum. good luck
Your car has an automatic transmission which includes a "neutral safety switch" to prevent the car being started while the shifter is in any position except "neutral" or "park". This switch is activated by the shift lever and prevents voltage to the starter solenoid when the car is in gear (drive or reverse). This is a safety features that prevents the car from lurching ahead or backward while starting.
A motor mount is just a part holding the motor to the frame of the car. It helps holds the motor in place so when you shift into gears the engine doesn't want to fly out of the car.
your shift motor on transfer case is probaly no good and needs to be changed or is also called encoder motor