Have 2000 Neon with 2.0. When I turn key to run position, more often than not car does not start. There is a slight grunt not a thump. Other times there is no noise at all. Battery and alternator checked out ok; starter relay ok, new ground stray to body and battery installed. Fluid levels ok. I put headlights on and someone else trys to start car. Headlight intensity remains bright.

Sometimes I switch the fan relay with starter relay and car may starts. Not all the time. Not sure if this means anything. Can anyone give some advise? Would appreciate.