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My van had probelms starting. Solenoid would click on and off like a machine gun when you turned the key over. New solinoid didn't fix the problem. Pulled the starter and tested it with voltmeter, it was shorted. Bought a rebuit one and it worked great until last week. Same problem.
Why is this happening? Only commonality I see is that the battery died after I left the ignition in the on position prior to both failures.
I assume that you're referring to the starter relay and not the starter solenoid. Starter relay is up near the battery, starter solenoid is part of starter.
Usually when the starter relay clicks on and off like that it's due to low battery amperage. I'd check the battery for a bad cell. Leaving the ignition in the "Run" position will after a considerable time pull down the battery (unless you also leave the headlights on) because you have several things that have power all the time, i.e. the EEC module keep alive memory circuit, the radio's presets, etc. But they pull little amperage and I think it would take a while to pull a good battery down that far.
My van had probelms starting. Solenoid would click on and off like a machine gun when you turned the key over.
Turn the headlights on, and then try to start the truck. If the headlights go completely out, then you have a battery problem or a bad connection at the battery or the ground at the engine block.
If the headlights stay bright, but the truck won't start, I would suspect the new starter, or the connection at the new starter.