That battery terminal looks a bit sad, of course, but not too poor to still use. That is assuming that broken area is not where a smaller wire (about AWG 10) was attached... Take a look down below where that terminal would be for a dangling wire.. If no wire, and battery voltage is 14V or better at idle, I would dismiss the battery/charging as a possible problem.
That info nickb2 posted has the solenoid resistance and pin-out at the trans connector, I would certainly check that; should be pretty easy to do.
That info nickb2 posted has the solenoid resistance and pin-out at the trans connector, I would certainly check that; should be pretty easy to do.