My 2003 dodge neon sxt decided to just die on me the other day... I have lights and my battery is good but my car will not turn over nor will my fuel pump engage like it should when the key is turned. I think it may be something electrical. what could it be

Nikki is the engine light on, are there any codes,have you had a tune up or any other work done lately.when you say it won't start when warm(do you mean engine will not turn over, or does engine turn and refuses to fire.
If I had to guess failing fuel pump, they tend not to build fuel pressure when ran a while(warmed up) and when left to cool build somewhat better pressure.
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Is Your Fuel Pump Going Bad
How do know if its fuel filter or fuel pump that is causing the problem
How To Diagnose Fuel Pump Failure EricTheCarGuy
http://www.clarks-garage.com/shop-manual/ts-01.htm#hot-start

2003 neon shaking after changing both right motor mounts ...

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BAD COMPRESSION CHECK COMPRESSION ON ALL CYLINDERS

Ok, even if the battery is new, get a voltmeter and measure the battery, if its below 12v, thats the problem. That way you completely eliminate all these factors without a doubt. Also check negative wire from battery to the ground box and connections. It sounds more like a corroded terminal.

change fuel filter & air filter

Possible defective wire harness on the engine or a defective computer.

Remove fuel pump fuse or relay, start engine till it dies, now there no more fuel pressure.You can now replace fuel filter or what ever you were going to do.

I HAVE ACTUALLY SEEN THE POSITIVE BATTERY CABLE ITSELF BECOME FAULTY ON THESE VEHICLES..CHECK FOR LOOSENESS OF WIRES RIGHT AT BATTERY CLAMP..ALSO CHECK BATTERY CONNNECTIONS AT UNDERHOOD FUSEBLOCK AND AT STARTER SOLENOID..

could be a lose ground somewhere. check the wires from your batery and alternator. specifically the grounds. no ground no power.