4.0 S TYPE CRANKS WON'T START

You should have read the manual you cannot push start all vehicles you can damage them. Try a known good charged battery first.

These links may help:
How to start your car with bad battery or starter Car will not start trouble shooting guide wont crank wont turn over etc... Troubleshooting and Fixing Car that Won Start Common Car Battery Issues That Cause Starting Problems

If it's been sitting for 3 years I would do as follows
1. Drain tank of all gas, give it some fresh gas.
2. Change the Spark Plugs
Attempt to start it. (Keep in mind it may take a few times to get all that old gas out of the lines)
Sitting it the worst thing for a rig. I advise never let it go without starting it ATLEAST once a month
If that doesn't work make sure it is getting fuel to the motor.
If so it could be your Distributor or Coil. Good luck

wont crank or wont start.??
no car starts , if it cant crank. (unless push starter (M/T magic)
that is not a trans sensor its the PRN switch.
ill answer for, wont CRANK !
it wont crank even with a good battery (charged) or jump started.
1: bad start
2: bad wires to same.
so hot wire the starter small wire, the key start line is tiny.
cranks. , starter good, no crank starter bad or cables bad.
if it cranks hot wired, then the key line is dead.
easy, huh?

not sure what you said but.
seems the battery is discharging,? 12.6v is fully charged,
own a voltmeter?
try a good loaned battery , does it start the car,?
i think you meant?
i can jumper cable start my car at any time. (off another running car)
but after running my car, the battery discharges and it will not crank at all. right?
this means ,the charging system on your car is bad.
if the starter cranks great, then the engine is flooded or is in great need of a tune up (sparkplugs etc)
if flooded try the super secret in the op guide, crank with throttle wide open , this magic trick cuts all fuel injection allowing the flooding
to purge away, and eventual starting.
my guess 2 is the car wont start, so you crank the battery flat
you jumper start it and it runs. (luck)
then day 2, same deal cranks ok but wont start.. ever tune up the engine?

check fuses ( main fuse engine fuse ignition fuse )

Duplicate entry

Sound like a wire loose. could be the earth cable to the engine, or the main power cable from the battery to the fuse box/ignition switch/starter.

Check fuel pressure at the injector rail. If good, suspect crankshaft position sensor--when it fails to start, check for sparks by pulling an ignition wire off the coils and holding it close to the coil with an insulated tool while someone cranks the engine. If no sparks, replace the sensor.

Running so few miles has accelerated the aging of the battery - the battery never had a chance to fully recharge in such small trips -  so now you have to replace it a year sooner than usual.
Just replace it.

If checking battery cables and wiring to the starter and ground points doesn't help. Have the battery checked for a bad cell. Preferably before you charge it.