I don't blame you for not wanting to get under the car in 110 degree weather but the best way to see what is going on is to get to the starter and check it out. The best way to see if it is the starter would be to jumper across the contacts on the solenoid and see what happens. If it engages then the problem is electrical if not then the issues lie in the electrical wiring or the ignition switch circuit. Good Luck!