I've got a 2007 Liberty with a good battery and starter, all lights and fuel pump light up upon turning key to on position. When the key is advanced to the start position the starter engages, and bumps the engine forward, but doesn't move it more that a fraction of a turn and then stops. Repeated turns to start and it moves forward, but just barely. If I pull the starter relay and jump the contacts there, it turns like it would be expected to to start, but doesn't start. Does this ring any bells?
First swap over the Starter Relay with an identical one nearby.
Jumping pins 30 and 87 together briefly in the Starter Relay Socket overrides the Starter Relay, Ignition Switch, the Actuator Pin assembly that moves the switch and the Park and Neutral Sensors.
So try start it in Neutral instead of Park.
The Ignition Switches are pretty robust but the Actuator Pin Assembly that rotates it is prone to break off at the tip...there is enough strength left in the tip to turn ignition lights ON but not enough strength to rotate the last bit against spring to move onto the Start position.
Best to remove the plastic covers over the steering column...two Female Torx screws.
Then remove the Actuator Pin Ignition Switch off the Actuator Pin Assembly....held on by a smaller Torx screw. This Torx screw is a Security Screw which requires a Male Torx Driver with a hole down its center.
If you see debris falling off the tip of the Actuator then it has failed.
Put the Jeep into Neutral and Park and the chipped key into the ignition slot and turned to release the steering lock.
Make use of a small flat screwdriver to rotate the slot in the ignition switch...ignition lights should come ON and the engine should rotate and hopefully start. If it starts then you can drive it like this until you get a new Actuator Pin Assembly from Dorman.
If it still does not fire then swap over the ASD Relay, check for CEL codes and make sure the Red LED on the left of the cluster for the Skis anti-theft is not flashing or ON solid.