No crank, no start. Battery just replaced, connections good. Engine repalced.

The crank sensor only comes into play while the engine is cranking or running to tell the computer where TDC is.
A no crank issue would be only the starting or security system.
Do you have battery power at the starter when the key is in the start position ? Are the battery cables clean and tight on both ends ?

no cranks, (A/T or M/T?)(
battery lugs cleaned?
Key turned on , CEL glows in dash, Check engine light>? yes, good.
does car crank jumper cable started.??????
if yes, your battery is bad or discharged, (good batteries can just be discharged, discharged dont make them bad, only dead or weak)
if ,jumper fails, to crank it fast.
then hot wire the solenoid (on side of starter caseing)
key in pocket, '
jump the big lug to the very tiny lug on the solenoid
cranks , not? bad starter
yes cranks but dont run, good, key is in pocket for safety, this is normal
but the KEY line is dead.
bad PRNDL switch
see the tricks section here

http://www.fixkick.com/nocrank.html#tricks

fuel filter,fuel pump.battery connection.

Check the coil see if ur getting power to it

No crank means dead battery, jump it or get a new battery. If your battery was not dead and you didn't get fuel or it did not start you would get a cranking noise and no starting

is the battery rated for enough cold cranking amps, to turn engine over fast enough in cold weather!

crank no start? I would check for fuel pressure on these models, the fuel pump module is quite often repalced. Then I would check ignition cap and rotor. Cap get white with corrosion and rotor green.

If the connections from the battery to the starter solenoid is good, the ground of the battery is good and the ground of the engine is good then the starter must crank well.
If there is slow cranking it is due to a faulty flywheel connection to the starter pinion, a tight engine/ faulty timing setting..... assuming that the battery and starter motor is double checked.

1- If engine is not cranking but hearing a click then

a- Problem with battery.

Try to jump start then if battery is over 5 years, replace battery

b- Solenoid works but not the starter.

Need to repalce the starter.

2- If engine is cranking but not catching on, then the problem is with the Bendix part. it is an intergrated part of the starter.

Replace the starter.

If you have the 4.0l inline 6 and you mean buy "cuts off" that the engine stalls at the stop light or refuses to start from time to time...this engine has a well know problem with the crank position sensor, if it is bad or the connection loose or incorrect, you will have this problem