2002 trailblazer randomly won't start. Good battery. Lights, radio all turn on.

Security system does NOT disabled the starter... Only the fuel injection system!!... Suspect failing alternator, battery or both.. Possible parasitic load on battery while vehicle is parked... Testing is required to confirm.

02 trailblazer, started this morning, just shut off. Dash lights on till hit key, then go out, good battery, just put new key switch on, will not turn over. Can jump solenoid to turn over and still won't start with key on. Idea ?