Loss of Electric to the dash

From what I understand the wiring harness connector (engine compartment) is prone to having issues over time. if I'm not mistaking, the power to the dash comes from a red?? wire within the harness. I'd start by checking if you have power before and after the connector. I'm getting ready to swap mine out due to a couple of these pin failures. But you may be able to fix the issue by thoroughly cleaning the contacts and apply some dielectric grease to help with further corrosion.

Sounds like whatever cable you're disconnecting and reconnecting has a lousy dirty connection that can pass a small amount of current like the current to the coil in the solenoid but not a large amount of current like what the starter draws..

I'd combine the 2 posts above and use the diagram below to give all your cable connections a good cleaning to prevent future problems too,and don't forget the spot where the negative battery cable is bolted to the block

When you're done you'll understand your electrical system a lot better

Diagram courtesy of TRB productions It should be just like your wiring