Chevrolet Repair: 2002 Chev. S10 pickup 4 cy., starter solenoid, s10 pickup

Question
i have a 2002 S10 chevy pickup.I can drive it starting and stopping when I cut it off several times, then it wont crank leaves me stranded for a couple of hours, seems like when it cools it will crank.Parts store said it was safety neutral switch but, it still  does the same thing just getting worse. Please help.

Answer
HI CHRISTY, WELL YOU WILL NEED TO DO SOME DIAGNOSTIC WORK FOR ME BEFORE I CAN TELL YOU WHAT IS GOING ON HERE. WHEN THIS HAPPENS CK TO SEE IF THE HEADLIGHTS COME ON,THIS WAY WE CAN KIND OF RULE OUT THE BATTERY OR CONNECTIONS..THE BEST WAY TO TELL WHAT IS GOING ON IS TO GET A 12 VOLT TEST LIGHT [CKS FOR 12 VOLTS AT A CONNECTION..]NOW FOR THE FUN PART,WHEN THE ENGINE WILL NOT CRANK OVER GET YOUR TEST LIGHT AND GROUND THE ONE SIDE TO A VERY GOOD GROUND SOURCE, SUCH AS THE FRAME, ENGINE, ALTERNATOR BRACKET WHAT EVER IS A GOOD GROUND,NOW TAKE THE TEST PROBE AND TOUCH THE POSITIVE SIDE OF THE BATTERY,IF THE GROUND IS GOOD THE LIGHT WILL LIGHT. NOW THAT WE KNOW THAT YOU HAVE A GOOD GROUND GO UNDER THE TRUCK AND YOU WILL NEED SOMEONE TO TURN THE IGN KEY TO THE CRANK SIDE OF THE SWITCH WHILE YOU TAKE THE TEST PROBE AND HOLD IT TO THE PURPLE WIRE ON THE STARTER SOLENOID. THIS WILL BE THE SMALL WIRE.IF THE LIGHT LIGHTS AND ENG DOES NOT CRANK THE STARTER IS BAD..TRY TO TAP THE STARTER WITH A SMALL HAMMER WHILE THE KEY IS HELD ON TO SEE IF IT CRANKS. AGAIN IF IT DOES THE STARTER IS BAD..NOW IF YOU HAVE NO POWER ON THIS PURPLE WIRE THEN YOU MAY HAVE A BAD IGNITION SWITCH OR CLUTCH INHIBITOR SWITCH IF A MANUAL TRANSMISSION OR STARTER RELAY..IF AUTOMATIC POSS IGN SWITCH OR AS YOU SAID NEUTRAL SAFTY SWITCH. THIS ARE ADJUSTABLE TO A POINT. TO RULE OUT THE STARTER AND BATTERY CONNECTIONS WHEN THIS HAPPENS YOU COULD JUMP THE SMALL PURPLE WIRE TO THE MAIN POS BATTERY CABLE BOLT TO THE STARTER. IF THE BATTERY AND CONNECTIONS AND STARTER  ARE ALL GOOD, THEN THE STARTER WILL CRANK LIKE THIS. USE A SCREW DRIVER OR WHATEVER YOU HAVE THAT IS METAL TO JUMP.. IF YOU HAVE THE KEY ON THE ENG WOULD START LIKE THIS, SO BE CAREFULL. LEAVE THE KEY OFF AND WHEN YOU JUMP THIS IT WILL CRANK OVER BUT WILL NOT START..I HOPE THIS HELPS YOU,LET ME KNOW HOW YOU MAKE OUT,GOOD LUCK,,TOM..