Re: Battery backwards
You have a voltmeter (multimeter)? Is that what you are using to tell if you have power? Then use it to figure out where the problem is. Check for voltage at each of the small terminals on the solenoid while somebody turns the key to the start position. You should have 12V on one of them and zeroV on the other, and the solenoid should click and the starter should run. If you have 12V on both small terminals, the safety switch is bad----OR the control is not set at start position as previously mentioned. If you don't have any voltage on either one, there is a problem with the ignition switch, or the wiring between the switch and the motor.
If it clicks but starter doesn't run, check voltage at the starter when the solenoid is clicked. Should have around 11-12V. If not, solenoid is bad. If you have ~12V and the starter doesn't run, the starter is bad. OR, the motor isn't grounded.
Before doing any of this, make sure your battery is good, and all cable connections are clean and tight. By clean, I mean shiny clean.
There is no voo-doo in electricity. It is all just good common sense and a bit of understanding how it works.