Hyundai Repair: 2001 Hyundai GX300, digital voltmeter, hyundai service

Question
QUESTION: I just purchased a 2001 Hyundai GX300 3 weeks ago.  Yesterday afternoon I parked it ran inside a store for about 10 minutes.  When I returned the car would not start.  The lights and bells came on but the car would not turn over at all.  It made no noise at all and there's no weird smells.  I tried to jump it but to no avail.  I went and purchased a new battery, installed it and it cranked immediately even before I tightened the connectors.  Turned it off to tighten them and it cranked again with no problem.  Everything sounded wonderful so we drove it home thinking the problem was solved.  Went out this morning and IT WILL NOT START.  I've checked the fuses and they all look fine.  There is a relay on the positive side of the battery cable but I don't know how to check that.  I don't understand how or why it would crank as soon as the battery was replaced but won't now.  

ANY AND ALL HELP WOULD BE GREATLY APPRECIATED!


ANSWER: It's not clear this is a battery issue, especially if the car doesn't jump start.  While the problem is occurring, read the battery voltage without load with a digital voltmeter.  It should be about 12.6 to 12.8V.  Then, read the battery voltage when attempting to crank the engine.  It shouldn't go below 9.0V.  If it does, you'll need to investigate why your battery is discharging-- possibly an alternator problem.

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QUESTION: We've ruled out the battery and the starter as being the problem; both were checked and are fine.  Also, the alternator has been ruled out as the batteries were fully charged when checked; not drained at all.  Seems sort of like the juice isn't getting from the battery to the starter.  I've located the starter relay switch but the Hyundai Service Center said they very rarely go bad - there's apparently no way to test them.  What else could it be.  I really don't think it's electrical as all of the electrical accessories work fine .. it just won't start up.  It still makes no noise at all except that you can hear the fuel pump engaging.  Any other suggestions ???

Answer
The dealer is right that the starter relays rarely fail.  But the last person I told that to actually had a starter relay problem.  Go figure.  If your starter relay is the same as other relays in the relay box, the strategy is simple.  Just swap it with another relay and see if anything changes.

My primary suspicion would be that you have a problem with your range switch (also known as an inhibitor switch or neutral safety switch).  Try starting in neutral rather than park.  If that's successful, the problem is with the switch or its adjustment.