[shorod]

What year is the Neon? Does it have any sort of antitheft system (factory or aftermarket)? You mention the starter does not engage, does the starter motor spin but doesn't turn the engine over? Are there any sounds such as a single click or rapid series of clicks? Have you removed the battery cables from the battery, cleaned them, and reinstalled, making sure they are snug? When you turn the key to the Start position do the typical electricals such as the radio, "idiot lights" on the dash, and blower motor turn off?

-Rod