Cranks but won't start sometimes. Also has cut out while idleing in traffic and again cranks but won't start. car has new battery.

Hi, what car you are talking about.

Could be a battery cable connection, faulty starter, or the neutral safety switch. You would need to know if you have battery power at the starter terminals when it fails to crank.

I assume you checked the fuel pressure and it is normal.
Are the spark plugs getting spark when it fails to start ?
Are you getting injector pulse from the computer ?
Any trouble codes stored in the computer ?

Park neutral safety switch maybe be the reason for the no crank ! Try putting the vehicle in park ,then try to crank the engine . Testing the electrical circuit is the best way to trouble shoot this problem , along with do a voltage drop test on the starter circuit ! This will test the battery cables an connections .
Starter Voltage Drop
How to voltage drop test starter motor circuit
Does it have a manual or automatic transmission ? Manual ? clutch switch . Looking at a wiring diagram I also see a starter cut relay !
http://www.bbbind.com/free_tsb.html Free wiring diagrams . Enter vehicle info. year , make , model and engine size . Under system click engine , under subsystem click starting . Then click the search button , then click the blue link ! Check the starter cut relay also . Videos on youtube showing how to test a relay controlled circuit !

are there any codes? have you checked the pressure in the fuel line. you may have a bad fuel pressure regulator. or a bad crank position sensor. spray starter in the throttle body and see if it starts

sounds like a bad crank position sensor

A battery from 07 is still decently new to be that bad, but I would check the alternator first, just get the car running and unhook the positive cable from the battery, if the car dies the alternator is bad.

No.
The crank sensor tells the computer when number one cylinder is at top dead center to find the timing for the spark plugs.
If the engine will not crank with the starter, the starter, key switch, battery or cables could be faulty.
Some of these items could also cause it not to start.
If the engine is stuck you won't be able to turn it at all.

replace main relay.