The problem turned out to be a broken green ground wire from the harness to the frame (where the battery's negative cable connects). I'd noticed the hanging wire when I first started troubleshooting, but it looked old and I knew I hadn't pulled it loose myself, so I figured it'd been there a while and I ignored it. When the new solenoid didn't solve my problem, I tested the old one (
) and it was fine. Remembering a similar grounding problem from one of my kid's cars a few years back, I decided to try reconnecting the ground wire and it worked (I think. It didn't crank all the way around but the starter engaged. My engine has a problem turning over when the piston is at TDC, so I have to crank it backward by hand sometimes to give it a running start.) Fingers crossed, though... I fee like it'll run now once I get it all put back together.
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