[ edit ]
I think you've got the wrong wires on the 'S' and 'I' terminals.
See the wiring diagram linked in my next post. The red w/ green wire should go to the '+' terminal on the coil, not the starter solenoid.
It sounds like the small red / green wire is trying to power the starter directly, and bypassing the solenoid contacts for the starter.
The amount of power needed to turn the starter & engine could nearly vaporize that small wire.
Solenoid wiring image below...
Depending on the under-hood location of the: battery, solenoid and starter, the large battery and starter cable connections on the solenoid can be reversed.
BUT, the wiring to the 'S' and 'I' terminals has to be as pictured below, no exceptions.
And/or you may need a new solenoid.
.