bad starter relay?

It is not that hard. It's a simple relay. The two large terminals are the contacts, and the BIG stud is also used for a junction point. The two small "push on" terminals are the coil

The coil is activated by the yellow wire from the key. It won't work unless the remaining small terminal is grounded by the neutral switch. Then the contacts close

The large terminal is battery, that contact closes and sends power to the "square" one and that feeds down to the starter solenoid, and activates the starter.