The car cranks and starts sometimes, the other times it will not crank. It will always crank when jumped.
The battery was swapped for a new battery while looking into this problem.
I was able to sit in the car and deliberately start it, turn it off and start it again until it didn't want to start anymore.
I noticed that when it did start, I heard the starter and/or ignition relays clicking. When it did not start, I heard nothing.
I've cleaned battery contacts and retightened them also replaced the metal connector that goes from the positive battery terminal to the fusible link.
Any ideas?

2004 G35 Manual Transmission.

 

Check the connections on the starter and the cable from the battery to the starter for corrosion.

 

If it only happens when the ENGINE IS HOT but will start again once the engine has cooled down then it's usually the starter. Starter solenoids fail like that when they age, heat soaked and they won't work until they cool off.

 

Here's the update. The problem was the starter. It bench tested fine when under no load, but would not start when connected to the gears. I also extended the the electrical lines from under the car and connected the starter, but without and connecting it to the gears and it would work like that too. Before doing any of that I tested voltage across both starter terminals and ground and got proper voltage. I figured the starter motor was too rigid to turn the flywheel, but would rotate when there was no load. Got a remanufactured starter from autozone, installed it and it fired right up. This was the first time I saw a starter that benched tested ok, but would not work when connected to the flywheel.

 

Glad you got it all sorted out.