2000 Dodge Neon Car not turning on.

Engine Performance problem
2000 Dodge Neon 4 cyl Automatic 115000 miles

Hi, I am hoping you guys could help me. About two nights ago, during the fall of a huge snow storm, I attempted to start my car up and did so successfully. However, as my girlfriend stepped on the gas several times in attempts to "warm up the car" while I removed the snow from the windshield the engine shut off and since then will not start at all. When I turn the key in the ignition I can feel rattling in the steering wheel (as though the car would like to start), all lights will come on ruling out the battery. All turns on except the engine. What do you think the problem is? What do you suggest I do to fix it? Thank you guys! I appreciate it.