Most times you can wiggle the shifter to trick the neutral switch into working. I would look closely at the starter solenoid it may be going out.
Make sure that it has petrol in it. If the engine turns over just fine,and only not start,it is not the starter solenoid or the neutral safety switch or the battery. First check to make sure that you can hear the fuel pump running when you first turn on the key. If no sound,check the fuses to the fuel pump and ECM. Check BOTH fuse blocks,side of dash and under hood. I would be thinking fuel or fire. The easyer of the two is check fire.Take the coil cover off top of engine,hold the coil outlet pens close to intake cam housing,have someone turn the key.If you see sparkes it is getting fire.If no sparks it will PROBABLY be the ICM (Ignition Control Module) Its pluged into that top cover you just took off. BUT,If you have fire,NOW you have to check fuel pump fuses.On these 2.4 DOHC engines,they don't have a good way of checking fule pressure so what I did was to make a tool to fit where the fuel filter is.I remove the filter insert my homade rig with a guage on it and turn it on. Key on,engine not running..41 to 47psi..engine idling W/pressure regulator vaccumm hose connected...31 to 44 psi and with vacuum hose disconnected..42 to 50 psi ,, injector resistance 11 to 13 ohms AND IT COULD BE DEFECTIVE CRANKSHAFT SENSOR. There are a couple other things it COULD be but check these thing first...Good luck www.autozone .com has repair manules online,check it out.It might be what you could use.
Try putting it in neutral and try.
I just had the tranny rebuilt in my 2000 Impala. When the mechanic was taking it apart, he showed me the neutral safety switch and it is inside the transmission. I think he told me that was the case for the 2000 and the 2001 Impala's. In that case the transmission has to come out in order to change the neutral safety switch.