Forget the starter. That has nothing to do once the engine is running. The dimming headlights and confused computers / warning lights are the classic symptoms of a failed charging system. Charge the battery at a slow rate for an hour, then once the engine is running, measure the battery voltage with a digital voltmeter. You must find between 13.75 and 14.75 volts. If it is low, suspect the alternator, but there are a couple of quick tests to verify that before you spend money on unneeded parts.
You said there's no voltage on the starter's solenoid wire, but you didn't say when. Are you expecting it to be there when the ignition switch is in the "run" position?
Saturday, February 28th, 2015 AT 1:07 PM