2006 grand prix no crank no start no click

Ran into this problem. Replaced the ignition switch,
as well as the starter, car ran fine for a day or so.
Now when I go to start i got nothing it seems like I
have melted the inside of solenoid, the starter
itself was not hot. But the solenoid was blazing
hot. Am about to do a new starter again any advice
on where i should go if this 3rd starter fails?
Also, intermittently can hear the throttle blade
open/closing with key off. Am assuming its a
wiring issue but i am lost.